how to solve the following question? Tickets numbered 1 to 20 are mixed up together and then a ticket is drawn at random. What is the probability that the ticket has a number, which is the multiple of 3 or 7?

If I throw a die what is the probability that I will get a number greater than 4?

A card is drawn from an ordinary pack and the gambler bets that it's a spade or an ace. What are the odds against winning the bet?

in this test how is the answer for the question: what is the probability of a coin getting tail and the answer came 1 i nstead of  the correct answer 1/2

S = {1,2,3,4,6}

n (S) = 6

A { 1,2}

n (A) = 2

P (A) =

## Card marked with number 3, 4, 5, .........., 50 are placed in a box and mixed thoroughly. A card is drawn at random from the box. Find the probability that the selected card bears a perfect square number.

Possible  outcomes are  4, 9, 16, 25,36,49, i,e 6.

P (Perfect square number ) =

## What is the probability that a non-leap year has 53 Mondays ?

There are 365 days  in a non-leap year.

days  = 52 weeks +1 day

one day can be M,T,W,Th,F,S,S  = 7

P (53 Mondays in non-leap year) =

## If the probability of winning a game is  find the probability of losing the game.

The probability of winning  the game

Probability of lose the game

## If P (E) = 0.20, then what is the probability of not E  ?

P (E) = 0.20

P (not E) 1- P (E)

= 1-0.20

=0.80

## A girl calculates the probability of her winning the game in a match and find it 0.08. What is the probability of her losing the game?

P (Winning the game) = 0.08

P (Losing the game) = 1-0.08 = 0.92

## In tossing a die, what is the probability of getting an odd number or number less than 4?

Odd numbers   = 1, 3, 5,

Number less than 4 = 1,2,3,

P (an odd no.or a no.<4)

## In tossing a die, what is the probability of getting an odd number or number less than 4?

Odd numbers   = 1, 3, 5,

Number less than 4 = 1,2,3,

P (an odd no.or a no.<4)

## In tossing a die, what is the probability of getting an odd number or number less than 4?

Odd numbers   = 1, 3, 5,

Number less than 4 = 1,2,3,

P (an odd no.or a no.<4)

## Two different dice are tossed together. Find the probability. (i) That the number on each die is even  (ii) That the sum of  numbers appearing on the two dice  is 5.

(i)  Even numbers  occur is (2,2) (2,4),  (2,6), (4,2), (4,4) (4,6), (6,2) (6,4), (6,6)

P  ( number of ech die is even ) =

(ii)  Sum of numbers  is  5 in (1,4) (2,3) (3,2) (4,1)

## A bag contains  3 red, 4 green and  5 white candles, one candle is drawn at random from the bag, find the probability that candle is not red.

Total number of candles  = 3+4+5= 12

P (candled is red ) =

P (Candle is  not red ) = 1- P (Candle red)

## One card is drawn from a well-shuffled deck of  52  cards. Find the probability of getting :  (i) a non- face card (ii) a black king

Face cards = 12

(i)  P (non-faces) =

(ii)  P (Black king) =

## Two dice  are thrown together. What is the probability of getting a doublet ?

Total number of possible outcomes  = 62 = 36

E : (Doublets are (1,1) (2,2) (3,3) (4,4) (5,5) (6,6)

Out comes   favourable to E = 6

P  ( a doublet)

= Number of outcomes favourable to E

Total number of out comes

## A bag contains 5 red balls and some blue balls. If the probability of drawing  a blue ball is double that of a red ball, determine the number of blue balls in the bag.

Let the number of blue balls  = x

Total number of balls  = x+ 5

Number of red balls = 5

## Three different coins are tosed together. Find the probability of getting  (i) Exactly  two heads  (ii)  at least two heads  (iii) at least two tails.

Sample  space for three coins  tossed is

{HHH,HHT, HTH,THH, HTT, THT, TTH, TTT}

n (s) = 8

(i)  Exactly two heads  = {HHT, HTH, THH}

n (P1) = 3

P1

(ii) At least two heads  {HHT,HTH, THH, HHH}

(iii) At least two tails  {TTH,THT,HTT,TTT}

n (P3) = 4

## There are 100 cards in a bag on which numbers from 1 to 100 are written. A card is taken out from the bag at random. Find the probability that the number on the selected card  (i)  Is divisible by a and is a perfect square (ii) Is a prime number greater than 80.

Sample space = {1,2,3.....99,100}

(i) Number divisible  by and perfect square are

A  = {9,36,81}

n (A) = 3

Requared probability  P (A)  =

(ii) Prime numbers greater than 80 and less than 100 are B  = {83,89, 97}

Required probability P (B) =

## A coin is tossed 500 times with the following observations: Head: 245 times, Tail: 255 times  The coins is tossed again. The probability of getting ahead is a ..............

The probability of getting a head  =

## A coin is tossed 1200 times with the following outcomes : Head : 455, Tail: 745 Compute the probability for each case.

Probability of getting tail

## Two coins are tossed simultaneously 500 times, following are the outcomes  No head = 100 times One head  = 200 times  Two heads  = 200 times If the two coins are simultaneously tossed again, Compute the probability of obtaining : (i) One head (ii) Two heads

Total number of outcomes = 500

Let E1 and E2  be the events of one head and two heads respectively,

## A die is rolled 200 times and its outcomes are recorded below: Outcome        1     2      3      4      5      6 Frequency    25   35    40    28    42    30 (i)  An even prime Find probability getting  (ii) A multiple of 3.

(i) An even prime number i.e., '2'
P (getting an even prime number)

(ii) Multiple of 3  i.e., 3 and  6

(getting multiple of 3)

## Teachers and students are selected randomly to make two teams of 20 members each on sports day to participate in the event of '' tug of war''. The  numbers of volunteers are as follows:         Teachers                                                Students  Male        Female                                   male       female   12             18                                       20            10    Find the probability that the person choosen at randomly  (i) is male  (ii) is a female student

Teachers                                                Students

Male        Female                                   male       female
12             18                                         20             10

Total number of volunteers = 12+18+20+10

= 60

Total number of males = 12+20 = 32

(i)  P  (Person is male)   =

(ii) P (Person is female student)   =

## Two coins are tossed 100 times with the following frequencies of different outcomes: Outcomes    2 head       1 head      No head Frequency     30               48            22                                                  Find the probability of getting less than 2 heads.

Probability getting less than 2 heads

= Number of times 0 or 1 head appeared

= 48+22= 70

Hence,

## A die is thrown 1000 times the frequencies of outcomes 1,2,3,4,5 and 6  as given below: Outcome         1             2             3          4                5             6 Frequency       179         150        157      149            175        190 A die is thrown once again . Find the probability of outcome '' greater than3'.

Total number of outcomes = 100

Number of outcomes  greater than 3

= (149+175+190)

= 514

Required probability =

## A die is rolled 300 times and following outcomes are recorded: Outcome       1         2         3         4        5      6  Frequency     42       60      55        53     60    30 Find the probability of getting a number more than  4.

frequency of outcomes of number more than 4

=60+30=90

P (getting a number more than 4)

## Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:   Outcome       3 heads         2heads        1 heads           Noheads          Frequency     28              72                   72                     28 Find the probability of getting 2 or more heads

Total outcomes = 200

Number of times 2 or more heads occur 28+72 = 100

Required probability =

## On a particular day, the number of vehicles passing through a crossing is given below: Vehicle           2 wheeler         3 wheeler      4 wheeler          Frequency           57                 33                        30 A particular vehicle is choosen at random. what is the probability that it is not a four wheeler

Total number of vehicles = 57+33+30=120

vehicles which are not four wheelers

= 57+33 = 90

P (Choosen vehicle is not four wheeler )

## The table given below shows the marks obtained by 80 students of a class in a test with maximum marks 100:  Marks                  0-20      20-40      40-60        60-80     Above 80 No.of students     8              16           40               10              6 A student is choosen at random. Find the probability that he gets: (i) less than 40 marks  (ii) 60% OR more marks.

Total number of students =80

(i) Number of students getting less than 40 marks

=8+16= 24

P (less than 40 marks) =

(ii) Number of students getting 60 or more than 60

P(60 or more than 60 marks)

## The following table shows the marks obtained by 30 students in a class test:    Marks obtained       70      58     60      52     65   75   68 No. of students       3        5       4        7       6      2     3   Find the probability that students score: (i) 60 marks (ii) Less than 60 marks

Total number of students  = 30

(i) Students getting 60 marks = 4

Probability of getting 60 marks =

(ii) Students getting less than 60 marks  = (5+7)= 12

Probability of getting less than 60 marks

## A and B  are the only two outcomes of an event.   probability of (A)  = 0.72,  then what will be the probability of (B) and why?

Since, P(A) +P (B) = 1

P(B) = 1-0.72

= 0.28

Because sum of probabilities is  1.

## In a group of 70 persons there are  15 boys, 20 girls,30 men and rest women. Find the probability that a selected person is a woman.

No. of women = 70-(15+20+30)

=5

P(Women) =

## In a cricket match, a batsman hits  boundary in 20% of the balls he played. Find the probability  that he did not hit a  boundary

Hits boundary = 20% of baalls

Does not hit boundary  = 80% of balls

P (not hitting boundary )

## Elevan bags of wheat flour,each marked 5 kg actually contained the following weight of flour in kg: 4.97, 5.05, 5.08, 5.03, 5.00, 4.86, 5.08, 4.98,5.04, 5.07, 5.00 Find the probability of a bag chosen at random which  contains more than 5 kg of flour.

Total bags = 11

More than 5 kg of flour  = 6

prob. of more than 5 kg of flour =

## Out of 200 bulbs in a box, 12 bulbes are defective. One bulb is taken out at random from the box. What is the probability that the drawn bulb is not defective?

Total number of cases = 200

Favourable cases  = 200- 12 = 188

Required probability  =

## A card is shown at random from a well-shuffled packs of 52  cards. Find the probability of getting neither a red colour nor or queen.

Total number of cards = 52

Number of read cards  = 26

Number of queens which are not red = 2

Cards which are neither red or norqueen = 52 - [26+2] = 24

Required probability  =

## A letter of English alphabet is chosen at random. Determine the probability that the chosen letter is a consonant.

In the English language, there are 26 alphabets. Consonant are  21. The probability of chosen a conosonant  = 21/ 26

## 20 tickets, on which numbers 10 to 20 are written, are mixed thoroughly and then a ticket is drawn at random out of them. Find the probability that the number on the drawn ticket is a multiple of 3 or 7.

Total number of cases = 20

n (s) = 20

A =  favourable cases  = {3,6,7,9,12,14,15,18}

n (A) = 8

Required probability =  P (A)  =

## Two different dice are tossed together. Find the probability that the product of the number on the top of the dice is  6.

Product of  6  are (1,6) : (2,3); (6,1); (3,2)

No.of possible out comes  = 4

Total number of chances  = 6  x 6 = 36

P (Product of  6 ) =

## A game of chance of consist od spinning an arrow which comes to rest pointing at one of the numbers 1,2,3,4,5,6,7,8  and these are equally likely outcomes. Find the probability that the arrow will point at any factor of  8 ?

Total number of points  = 8

Total number of possible  outcomes

P  (Factor  of  8) = No of favourable outcomes

Total no. of possible outcomes

## Find the probability of an impossible event

P (Impossible event )  =

## A bag contains card numbered from 1 to 25 a card  is drawn at random from the bag. Find the probability that the number is divisible by both 2 and 3

The numbers divides by 2  and 3  both  = 6,12,18,24 = 4

P (number divisible by 2 and 3) =

## A number is selected at random from 1 to 30. Find the probability that it is a prime number.

Prime numbers are  = 2,3,5,7,11,13,17,19,23,29 = 10

No. Possible outcomes = 30

P (prime  no) =

## A box contains  90 discs, numbered from  1 to 99  if one disc is drawn  at random from box, find the probability that it bears  a prime number less than 23.

No.of possible outcomes  = 90

Primes less than 23 = 2,3,5,7,11,13,17,19

= 8

P (Prime no.less than 23) =

## From the numbers 3,5,5,7,7,7,9,9,9,9, one number is selected at random, what is the probability that the selected number is mean ?

Total Outcomes  = 10

Mean  =

P (Mean ) =

## A die is thrown once. Find the probability of getting a prime number

Total outcomes  = 6

Prime numbers  = 2,3, 5 = 3

P(Prime no) =

## The probability of getting a bad egg in a lot of 400 egg is 0.035. Find the number of bad eggs in the lot.

Here,  P (Bad eggs) = 0.035

Total no .of eggs

= 14

## A bag contains lemon flavored candies only. Shalini takes out one candy without looking into the bag. What is the probability that she takes out an orange flavoured candy ?

Bag contains only lemon flavoured candies.

P (Orange flavoured candies) = 0

P(E) + P(E) = 1

## The probability of winning a game is  1/3  less than  the twice of losing the game.Find probability of winning the game.

Let the probability of  winning  a game  = p

and the probability of losing a game  = q

we know that  = p+q = 1

According to question

On solving (i) and (ii)  we get

and

Probability of winning a game  =

## Following is the data about the months of birth of 40 students in class IX: Feb, Jan, July, June, March, Feb, Feb, Feb, Nov, Jan, Jan, Dec, May, June, Jue, July, June Nov, Dec, June, July, June, Aug, Dec, June, Mar, July, July, June, Dec, Sep, Marc, Jan, Dec, June, Dec, Sep, March, Jan, Nov. One student is chosen at random. ind the probability that the student choosen: (i)  Was born in June. (ii) Was not born in the month of June.

 Month Student Jan 5 Feb 4 March 4 May 1 June 9 July 5 Aug 1 Sep 2 Nov 3 Dec 6

(i) Let E1 be the event of the student born in June

(ii) Let E2 be the event of the student not born in June

Favourable outcomes  = (40-9) = 31

## The given table shows the month of birth of 40 students. (ii) Find the probability that a student was born in the month of February.(i) Find the probability that a student was born in the month with  31 days

(i)  P (a student born in a month with 31 days)

(ii)  P (Student born in February)

## Given below is the frequency distribution of salary (in rupees) of 80 workers in a factory. if a  worker is selected at random, find the probability thtat his salary is (i) Less than  Rs. 3000 (ii) More  than or equal to Rs. 1000 (iii) More than or equal to Rs. 2000 but less than Rs.4000

(i) The probability of getting a salary of less than Rs. 3000

(ii) The probability of getting a salary more than or equal to Rs., 1000

(iii) The probability of getting salary more or equal to 2000 but less than Rs. 4000

(i)

(ii)

(iii)

## A die is thrown  500 times. The frequency of numbers (1,2,3,4,5,6) appearing on the uppermost  face are given: Find the probability of having an outcome  (i)  Number of 3  on uppermost face (ii) Number greater than 4 (iii) Number  <4 (iv) Number between 1 and 3

(i) P (number 3)

(ii)P (Number > 4 )  =

(iii) P (Number <4)

(iv) P (Number between 1 and 3)

## A survey of 200 people was conducted about their preference of visiting various pavilions. Find the probability that selected person visited : (i) Both good living and Delhi pavilion. (ii) Only defence pavilion  (iii) Only toy pavilion  (iv) Both toy and defence pavilion

Total number of people  = 200

(i) P (Good living and delhi pavilion)

(ii) P (Only defence pavilion)

(iii) P (Only toy pavilion )

(iv)  P (both toy and defence)

## The weights of 60 persons in a  group are given below: Find the probability that a person selected at random has: (i)Weight less than 65 kg  (ii) Weight between 61 and 64 kg  (iii) Weight equal to or more than 64 kg

(i) P weight less than 65 kg  =

(ii) P (Weight between 61 and 64 kg)

(iii) P (Weight equal to or more than 64 kg)

## Fifty seeds were selected at random from each of 5 bags of seeds and were kept under standardised conditions favourable to germination. After 20 days, the number of seeds which had germinated in each collection was counted and recorded as follows: What is the probability of the germination of : (i) More than 40 seeds in a bag (ii) Less than 41 seeds in a bag (iii) 49 seeds in a  bag

(i) P more than 40 seeds in a bag

(ii) P(Less than 41 seeds in a  bag )

(iii)  P (49 seeds in a bag ) = 0.

## Two dice are thrown 400 times Each time sum of two numbers appearing on the tops is noted as given in the following table: What is the probability of getting a sum  (i) 5 (ii) More than  10 (iii) Between 5 and 10

(i)

(ii) P (More than 10)         =

(iii) P ( between 5 and 10)

## Marks obtained by 90 students in a particular subject out of a total of 100 are given below find the probability that a student selected obtained marks 60 or above and a student selected obtained less than 40. Number of students obtained marks 60 or above

= 15+8 = 23

P (Marks 60 or above) =

Students who obtained marks less than 40 = 7+10+10 = 27

P (Marks less than 40) =

## Following distribution gives the weight of 38  students of a class: Weight in kg             No. of students 31-35                           9 36-40                           5 41-45                          14 46-50                           3 51-55                           1 56-60                           2 61-65                           2 66-70                           1 71-85                           1  Find the probability that the weight of a student in the class is  (i)  At most  60 kg  (ii) at least 36 kg  (iii)  Not more than 50 kg

Total number of students = 38

(i) Number of students whose weight is at most 60 kg

= 9+5+14+3+1+2 = 34 kg

Probability that weight of a student is at most 60 kg

(ii) No. of students whose weight is at least  36 kg

= 5+14+3+1+2+2+1+1 = 29 kg

Probability that weight is at least 36 kg

(iii) No. of students whose weight is not more than 50 kg

= 9+5+14+3 = 31

Probability that the weight of a student is not more than 50 kg

## The following table shows the daily earning of 25 shops. What is the probability that a shop earns (i)  100 and more  (ii) At least Rs. 60  but less than 80. (iii) Less than 40

(i) P (Earning Rs. 100  and more ) =

(ii) P (at least Rs. 60 but < 80) =

(iii) P (less than Rs. 40) =

## In a mathematics test, 90 students obtained (out of 100) the marks given in the following table: (i) A student obtained less than  41.Find the probability  (ii) A  student obtained more than 50. (iii)A student obtained between 41 and 80.

(i)  Prob. of less than 41

(ii) Prob. of more than 50

(iii) Prob. of marks between 41 and 80.

## Following tha table show the marks scored by a group of 90 students in a mathematics test of 100 marks : (i) Less than  30A student is selected at random. Find the probability that student has obtained. (ii) 60 or more marks  (iii) between 40 and 70 marks  (iv) 70 or more marks.

(i) Prob. of less than 30 marks

(ii) Prob. of marks 60 or more marks

(iii) Prob. of marks between 40 and 70

(iv) Prob. of marks 70 or more

## The heights of the students of a class is measured and recorded as given below: A student is selected at random. Find the probability that height of the student  (i) More than 135 cm  (ii) at least 145 cm  (iii)  Less than 130 cm  (iv) 125 cm or more but less than 140 cm.

Total student = 7+7+11+3+5+9+8 = 50

(i)  P (Height of student is more that 135 cm) =

(ii) P (Height of student is at least 145 cm

(iii) P (Height of student is less than 130 cm

(iv)  P (Height of student is 125 or more but less than 140

## In class IX of 50 students, the second language opted by the student is as also follow: Sanskrit - 14 Japanese - 08 French - 12 Urdu -6 Rest of then opted for German  A student is selected at random. Find the probability that the student  (a) opts for French (b) Does not o[ts forJapanese. (C) Either opt for Sanskrit or German

(a) Prob. that a student selected is opts

French language =

(b) Prob. that a student selected does not opt for Japanese = 1- selected student opts Japanese

(C) Prob. that selected student either opts for Sanskrit or  for German = prob. of student opts

Sanskrit + Prob.of student opts. German

No. of student who opted German

Prob. that selected student either opt for Sanskrit or for German

## When a coin is tossed, the probability of getting a head is

When  a coin is tossed, the total number of outcomes

## If the probability of an event is represented by p, then   is true/false

Probability of an event associated with a random experiment lies between 0 and 1 (both included)

So given statement  is true.

## A die is thrown, what will be the probability of getting an even number

Favourable number of outcomes  = 3 (2,46)

Total number of outcomes  = 6

?Required probability =

## Alphabets A, B......., J written on the flash cards and kept in fishbowl. Arun is asked to take one flash card from the fishbowl. What is the probability of getting letters in his name?

Probability of getting letters in the  name ARUN from A to J = 1/10

## A  die is thrown once. The probability of getting an even number is a.             b.         c.         d.

d Probability getting outcomes

Probability of  getting even numbers  =

## The letters of the word MALAYALAM are written in a paper slip and put into a box. A child is asked to take one slip from the box without looking. a. What is the probability of getting the letter A? b. What is the probability of not getting A?

Given, the word MALAYALAM

a. Probability P(A) =

Hence, the probability of getting the letter P(A) = 4/9

b. The probability of not getting A = 1 - P(A) = 1 - 4/9 = 5/9

## There are 30 scouts and 20 guides in a school. In another school, there are 20 scouts and 15 guides. From each school, one student among them is to be selected for participation in a seminar. a. What is the total number of possible selection? b. What is the probability of both being scouts? c. What is the probability of both being Guides? d. What is the probability of one scout and one guide?

 Name of school Scout Guide Total A 30 20 50 B 20 15 35

Total number of possible selection  = m x n  (Fundamental  counting theorem)

a. m x n  = 50  x 35 = 1750.

b. Probability of both being scouts

c. Probability of both being guide = m x n

= 20 x 15 = 300 (F)

d.Probability of one scout and one guide

1 - P(S) + P(G) (Formula)

ie.,

## A box contains 8 black beads and 12 white beads. Another box contains 9 black beads and 6 white beads. One bead from each box is taken. a. What is the probability that both beads are black? b. What is the probability of getting one black bead and one white bead?

BOX - 1

Number of black beads = 8

Number of white beads = 12

BOX - 2

Number of black beads = 9

a. The probability of getting blackhead from the box - 1   =

The probability of getting white beads from the box -2 =

Hence the probability of getting both black =

b. The probability of getting 1 black bead from the box - 1

The Probability of getting I white bead from the box -2

Hence the probability of getting the 1 black and 1 white bead

## A card is drawn from a well shuffled deck of playing cards. Find the probability of drawing  a red face card.

Total outcomes = 52

Redface card  = 6

P(red face card) =

## Find the probability of getting a sum of 9, when two dice are thrown simultaneously

The two dice are thrown

Possible outcomes = 36

The sum of both faces be 9 they are,

(3,6); (6,3) (4,5) (5,4)  = 4

## Can 1.1 be probability of an event

No. since the probability of an event cannot be more than 1.

## A bag contain 6 red and 5 blue balls. Find the probability that the ball drawn is not red.

No.of possible outcomes  = 6 + 5

= 11  balls

P(not red) = 11 - 6 = 5

## There are 30 cards of the same size in a bag in which the numbers 1 to 30 are written. One card is taken out of the bag at random. Find the probability that the number on the selected card is not divisible by 3.

Total cards  = 30

Number of divisible by 3 = 3, 6, 9 , 12,15, 18, 21, 24, 27, 30 = Total number 1

i.

ii.

## Harpreet tosses two different coins simultaneously. What is the probability that she gets :  i.  Atleast one head ii. One head and one tail

Possible outcomes as HH, TT, TH, HT

i.

ii.

## A bag contains cards bearing numbers from 11 to 30. A card is taken out from the bag at random. Find the probability that the selected card has multiple is 5 on it.

No. of cards = 20

Multiples of 5 from 11 to 30 are 15, 20, 25, 30 (4 in number)

Required probability  =

## A bag contains 5  red, 8 green and 7 white balls. One ball is drawn at random from the bag, find the probability of getting: i. not a white ball,  ii. Neither a green nor a red ball.

Total balls = 5 + 8 + 7  = 20

i.   P (White ball) =

P (not white)  =

ii.  P (green or red) =

P (neither green nor red) =

## Two dice are rolled simultaneously. Find the probability that the sum of numbers appearing is 10.

When two dice are thrown

Possible outcomes  = 36

If sum of both faces should be 10, they are,

## In a family of two children find the probability of having atleast one girl.

Sample space S = GG, GB, BG,BB (Optional)

P(atleast one girl)

## Find the probability that a leap year has 53 sundays.

366 days  = 52 weeks + 2 days

2 days can be MT, TW, WTH,THF, FS,FS, SS, SM = 7

## Two dice, one blue and one grey, are thrown at the same time. What is the probability that the sum of the two numbers appearing on the top of the dice is 8?

Total number of outcomes  = 36

Favourable outcomes are (2,6) (3,5) (4,4) (5,3) (6, 2) = 5

Required probability =

## A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball from the bag  is thrice that of the red ball, find the number of blue balls in the bag.

Let blue balls  =  x and red balls = 5

Total balls  = 5 + x

P(red ball) =

P(blue ball) =

## Two coins are tossed together. Find the probability of getting both heads or both tails.

Possibilities are HH, HT,TH,TT

P(HH or TT) =

## A lot consists of 144 ball pens of which 20 are defective and others are good. Nuri will buy a pen if it is  good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that: i.  She will buy it ii. She will not buy it

Total no of pens = 144

Defective one  = 20

Good ones  = 144 - 20 = 124

Probability of not purchasing pen  =

## What is the probability that there are 53 Wednesday in a leap year?

In a leap year number of days = 366 days

= 52 weeks  + 2 days

Two days can be SM, MT, TW, WTH, THF, FS, SS, =7

Out of these 7 calenders, two calenders will have 53 wednesdays

P (53 Wednesdays in a leap year) =

## From a pack of 52 playing cards, Jacks,, Queens and Kings of red colour are removed. From the remaining, a card is drawn at random. Find the probability that drawn card is : i. A black king,  ii. A card of red colour iii. A card of black colour

Total cards  = 52

Cards removed  = 6

Card .... = 52 - 6 = 46

Total black king  = 2

Probability of drawing black king =

Total red card  = 26 - 6 = 20

Probability of drawing red colour card =

Total card of black colour = 26

Probability of drawing black colour card =

## A bag contains cards numbered 1 to 49. Find the probability that the number on the drawn cards is : i. An odd number  ii. A multiple of 5 iii. Even prime

Total cards =  49

i.  P (odd number) =

ii. P(Multiple of 5) =

iii. P (even prime) =

i.

ii.

iii.

## A game consists of tossing a one -rupee coin 3 times and noting the outcome each time. Ramesh will in the game if all the tosses show the same result (i.e., either all three heads or all three tails) and losses the game otherwise. Find the probability that Ramesh will lose the game.

n(S) = 8

Same result on all the tosses (A) =

n (A) = 2

P(Ramesh will lose the game) =

## In a single throw of a pair of different dice, what is the probability of getting (i) A prime number on each dice? (ii) a total of  9  or 11?

i)  Favourable outcomes are (2,2) (2,3) (2,5) (3,2) (3,3) (3,5) (5,2) (5,3) (5,5) ie., 9 outcomes.

P (a prime number on each die)     or

ii. Favourable outcomes are (3,6) (4,5) (5,4) (6,3) (5,6) (6,5) ie., 6 outcomes

P (a total of 9 or 11)  =  or

## A box consists of 100 shirts of which 88 are good, 8 have minor defects and 4 have major defects. Ramesh, a shopkeeper will buy only those shirts which are good but 'Kewal' another shopkeeper will not buy shirts with major defects A shirt is taken out of the box at random. What is the probability that: i. Ramesh will buy the selected shirt? ii. 'Kewal' will buy the selected shirt?

i. Number of good shirts = 88

P (Ramesh buys the shirt) =

ii. Number of shirts without Major defect  = 96

## A box contains 100 cards marked from 1 to 100. If one card is drawn at random from the box, find the probability that it bears: i.  A single digit number ii.  A number which is a perfect square  iii. A number which is divisible by 7

(i) P (Single digit number) =

(ii) P (Perfect square) =

(iii) P (a number which is divisible by 7) =

## Cards numbered 2 to 101 are placed in a box.  A card is selected at random from the box, find the probability that the card selected: i. Has a number which is perfect square.  ii. Has an odd number which is not less than 70.

Perfect squares are 4,9,16,25,36,49,64,81,100

(i)  P (Perfect square) =

(ii) P (Odd number not less than 70) =

## All red face cards are removed from a pack of playing cards. The remaining cards are well shuffled and then a card is drawn at random from them. Find the probability that the drawn card is : i.  A Red card ii. A face card iii. A card  of clubs

Since the red face cards are removed

No. of red card  = 52-6=46

(i)   P (a red card) =

(ii)  P (a face card) =

(iii) P (a card of clubs) =

## Two different dice are rolled together. Find the probabity to getting: i. The sum of numbers on two dice to be 5. ii. Even numbers on both dice.

Total possible outcomes  : 36

(i) The possible outcomes are (2,3) ; (3,2) ; (1,4) ; (4,1)  = 4

Required probability P(E) =

(ii) The possible outcomes  are :

(2,2) ; (2,4) ;(2,6) ; (4,2) ; (4,4) ; (4,6) ; (6,2) ; (6,4) ; (6,6) = 9

Required probability

## The probability of selecting a red ball at random from a jar that contains only red, blue and red orange balls is . The probability of selecting a blue ball at random from the same jar is  if the jar contains  10 orange balls , find the total number of ball in the jar.

P(red ball) = , P, (blue ball) =

P(Orange ball) = 1 -

(Total no. of balls) = 10

Total number of balls =

## Two different dice are thrown together. Find the probability of : i. Getting a number greater than 3 on each die. ii. Getting a total of 6 or 7 of the numbers on two dice.

i. Favourable outcomes are (4,5), (4,4) (4,6) (5,4) (5,5) (5,6) (6,4) (6,5) (6,6)  ie., 9 outcomes

P (a number > 3 on each die) =

ii. Favourable outcomes are  (1,5) (2,4) (3,3) (4,2) (5,1) (1,6) (2,5) (3,4) (4,3) (5,2) (6,1) ie., 11 out comes

P (a total of 6 to 7)  =

## One card is drawn from a well shuffled deck of 52 cards. Find the probability of getting (a) Non face card , (b) Black king or Red queen, (c) Spade card.

(a) Total number of cards  = 52

Number of non face cards = 52 - 12 = 40

P(non-face cards) =

Number of black kings  = 2

Number of red kings  = 2

(b) P(a black kind or a red queen) =

(c) Number of spade cards  = 13

## Three coins are tossed simultaneously once. Find the probability of getting: (i) Atleast one tail (ii) No tail

Sample face =

(i) P(atleast one tail ) =

(ii) P(no tail) =

## A game consists of tossing a one -rupee coin three times and noting its outcome each time. Find the probability of getting: i. Three heads ii. Atleast two tails.

Total number of outcomes  =

ii) P (atleast two tails) =

## One card is drawn from a well shuffled deck of 52 cards. Find the probability getting: i. A red facecard ii. A spade iii. Either a king or a black cards.

Total outcomes  = 52

i)

ii)

iii)

## Three unbaised coins are tossed together. Find the probability of getting: i. Atleast two heads ii. Atmost two heads

The total number of possible outcomes = 8

## A bag contains, white black and red balls only. A ball is drawn at random from the bag. If the probability of getting a white ball is  and that of a black ball is  then find the probability of getting a red ball.If the bag contains 20 black balls, then find the total number of balls in the bag.

P (White ball) =  ;  P (Black ball)

P (Red ball) =  1 -

(Total no.of balls) = 20

Total number of balls  =

## A bag contains, white black and red balls only. A ball is drawn at random from the bag. If the probability of getting a white ball is  and that of a black ball is  then find the probability of getting a red ball.If the bag contains 20 black balls, then find the total number of balls in the bag.

P (White ball) =  ;  P (Black ball)

P (Red ball) =  1 -

(Total no.of balls) = 20

Total number of balls  =

## A bag contains 18 balls out of which x balls are red. i. If one ball is drawn at random from the bag, what is the probability that it is not red? ii. If 2 more red balls are put in the bag, the of drawing a red ball will be  times the probability of drawing a red ball in the first case. Find the value of x.

P(red ball) =

i) P(no red ball) =

ii) Total number of balls  = 18 + 2 = 20

Red balls are = x  + 2

P(red balls) =

Now, According to the question,

## Cards numbered 1 to 30 are put in a bag. A card is drawn at random. Find the probability that the drawn card is  i.  Prime number  > 7  ii. Not a perfect square

No.of possible outcomes  = 30

i. P (Prime no >7) = 11,13,17,19,23,29 = 6

ii. P (not a perfect square) =

## Two dice are thrown at the same time. Find the probability of getting: i. Same number on both dice ii. Sum of two numbers appearing on both the dice.

(i)

(ii) P(Sum is 8) =

## Five cards, ten, Jack, Queen, King and Ace of diamonds are well shuffled. One card is picked up from them. i. Find the probability taht the drawn card is Queen.  ii. If the Queen is put aside, then find the probability  that the second card drawn in an ace.

Total cards = 5

i) P (Queen) =

ii) P(Ace) =  (Since, Queen was kept aside)

## Cards marked with numbers 3,4,5...........,50 are placed in a bag and mixed throughly. One card is drawn at random from the bag. Find the probability that number on the card drawn is : i. Divisible by 7 ii. A perfect square iii. A multiple of 6.

Total number of cards  = 48

Probability of an event

Number of cards divisible by 7 = 7

P (Cards divisible by 7) =

Number of cards having a perfect square = 6

P(Cards having a perfect square) =

Number of multiples of 6 from 3 to 50 = 8

P (Multiple of 6 from 3 to 50) =

## A game of chance consists of spinning an arrow on a circular board, divided into 8 equal parts, Which comes to rest poiniting at one of the numbers 1,2, 3......8, which are equally likely outcomes. What is the probability that the arrow will point at (i) and odd number (ii) a number greater than 3 (iii) a number less than 9.

i.  Favourable outcomes are  1,3,5,7, ie., Outcomes

P (an odd number) =

ii. Favourable outcomes are 4,5,6,7,8 ie., 5 outcomes

P (a number greater than 3)  =

iii. Favourable outcomes are 1,2,3......8

P (a number less than 9) =

## A number x is selected at random from the numbers 1,2,3 and 4. Another number y is selected at random from the numbers 1,4, 9  and 16. Find the probability that product of x and y is less than 16.

Given,

Total number of possible products = 4  x 4 = 16.

Productsx.y which less than 16 are

Required probability

## All the red face card are removed from a pack of 52 playing cards. A card is drawn  at random from the remaining cards, afetr reshuffling them. Find the probability that the drawn card is  i. Of red colour  ii. A queen iii. An ace iv. A face card

i)

No. of crads remaining = 52 - 3 x 2

= 52 - 6 = 46

No.of red cards = 26 - 6 = 20

P (a red colour) =

ii)

No. of queen  = 4 - 2 = 2

P (a queen) =

iii)

No.of ace = 4

P (as ace) =

iv)

No. of face cards = 12 - 6 = 6

P (a face card) =

## All the black face cards are removed from a pack of 52 cards. Find the probability getting a,  i. Face card         ii. Red card iii. Black card     iv. King

Since all the black face cards are removed, the total number of remaining cards = 46

i.   P (Face card)   =

ii. P (red card)     =

iii. P (black card) =

iv. P (king card)   =

## A box contains 20 cards from 1 to 20. A card is drawn at random from the box. Find the probability that the number on the drawn card is: i. Divisible by 2 or 3 ii. a prime number

No.of possible outcomes = 20

i. Total no. divisible by 2 or 3 = 6, 12, 18 = 3

P(divisible by 2 or 3) =

ii. Prime numbers = 2,3,5,7,11,13,17,19 = 8

P (a prime no) =

## A box contains cards bearing numbers from 6 to 70. If one card is drawn at random from the box, find the probability that it bears. i. A one digit number  ii. A one number divisible by 5 iii. An odd number less than 30. iv. A composite number between 50 and 70

Total number of cards = 65

i) P (one digit number) =

ii) No. divisible by 5 = 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70 = 13

P (a number divisible by 5) =

iii) Odd no.less than 30 = 7,9,11,13,15,17,19,21,23,25,27,29 = 12

P (an odd number less than 30 ) =

iv) P (a composite number between 50 and 70) =

## A card is draw at a random from a well shuffled deck of playing cards. Find the probability that teh card drawn is: i. A card of spade or an ace ii. A black king iii. Neither a jack nor a king  iv. Either a king or a queen.

i)   Cards of spade or an ace  = 13 +  3 = 16

Total no.of cards = 52

P (Spade or an ace) =

ii)  Black kings = 2

P(a black king) =

iii) Jack or king  =  4 + 4 = 8

P (Neither jack nor king) =

iv) King or queen = 4 + 4 = 8

P(Either a king or a queen) =

## A bag contains 15 balls of which x are blue and the remianing are red. If the number of red balla are increased by 5, the probability of drawing the red balls doubles. Find: i. P (red ball) ii. P(blue ball) iii. P (blue ball it of 5 extra red ball are actually added)

According to the question,

blue ball = 12  and red ball = 3

i) P (red ball) =

ii)P (blue ball) =

iii) P (Blue ball is 5 red balls are added) =

## Three digit number are made using the digits 4,5,9 (without repetition). If a number among them is selected at random, what is the probability that the number will: i. Be  a multiple of 5 ? ii. Be a multiple of 9 ?  iii. Will end with 9 ?

Total number of three digit numbers are: 459, 495, 549, 594, 945, 954 = 6

i)   P (Multiple of 5) =

ii)  P (Multiple of 9) =

iii) P (ending with 9) =

## A number of x is selected at random from the numbers 1,2,3 and 4. Another number y is selected at random from the random from the numbers 1,4,9 and 16. Find the probability that product of x and y is less than 16.

We have

Total possible income = 1, 2, 3, 4, & 1,4, 9, 16 = 16

Total favourable event having product less than 16

= 9+1,2,3,4,4,8,12 = 7+1=8

## A number x is chosen from 25, 24, 23, -2, -1, 0, 1, 2,3 find the probability that

Favourable outcome  = 5

Total outcomes  = 9