# Solution of Chapter 13. Probability (RD Sharma - Mathematics Book)

## Exercise 13.1

1

The probability that it will rain tomorrow is 0.85. What is the probability that it will not rain tomorrow?

2

A die is thrown. Find the probability of getting:

(i) a prime number

(ii) 2 or 4

(iii) a multiple of 2 or 3

(iv) an even prime number

(v) a number greater than 5

(vi) a number lying between 2 and 6

3

In a simultaneous throw of a pair of dice, find the probability of getting:

(i) 8 as the sum

(ii) a doublet

(iii) a doublet of prime numbers

(iv) a doublet of odd numbers

(v) a sum greater than 9

(vi) an even number on first

(vii) an even number on one and a multiple of 3 on the other

(viii) neither 9 nor 11 as the sum of the numbers on the faces

(ix) a sum less than 6

(x) a sum less than 7

(xi) a sum more than 7

(xii) at least once

(xiii) a number other than 5 n any dice.

(xiv) even number on each die

(xv) 5 as the sum

(xvi) 2 will come up at least once

(xvii) 2 will not come either time

4

Three coins are tossed together. Find the probability of getting:

(iii) at least one head and one tail.

(iv) no tails

5

What is the probability that an ordinary year has 53 Sundays?

6

What is the probability that a leap year has 53 Tuesdays and 53 Mondays?

7

A and B throw a pair of dice. If A throws 9, find B’s chance of throwing a higher number.

8

Two unbiased dice are thrown. Find the probability that the total of the numbers on the dice is greater than 10.

9

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is

(i) a black king

(ii) either a black card or a king

(iii) black and a king

(iv) a jack, queen or a king

(v) neither a heart nor a king

(vii) neither an ace nor a king

(viii) neither a red card nor a queen.

(ix) other than an ace

(x) a ten

(xii) a black card

(xiii) the seven of clubs

(xiv) jack

(xvi) a queen

(xvii) a heart

(xviii) a red card

(xix) neither a king nor a queen

10

In a lottery of 50 ticket bears a prime numbered 1 to 50, one ticket is drawn. Find the probability that the drawn ticket bears a prime number.

11

An urn contains 10 red and 8 white balls. One ball is drawn at random. Find the probability that the ball drawn is white.

12

A bag contains 3 red balls, 5 black balls and 4 white balls. A balls is drawn at random from the bag. What is the probability that the ball drawn is:

(i) white?

(ii) red?

(iii) black?

(iv) not red?

13

What is the probability that a number selected from the numbers 1, 2, 3,…, 15 is a multiple of 4?

14

A bag contains 6 red, 8 black and 4 white balls. A ball is drawn at random. What is the probability that ball drawn is not black?

15

A bag contains 5 white and 7 red balls. One ball is drawn at random. What is the probability that ball drawn is white?

16

Tickets numbered from 1 to 20 are mixed up and a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 7?

17

In a lottery there are 10 prizes and 25 blanks. What is the probability of getting a prize?

18

If the probability of winning a game is 0.3, what is the probability of loosing it?

19

A bag contains 5 black, 7 red and 3 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is:

(i) red

(ii) black or white

(iii) not black

20

A bag contains 4 red, 5 black and 6 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is:

(i) white

(i) red

(iii) not black

(iv) red or white

21

A black die and a white die are thrown at the same time. Write all the possible outcomes. What is the probability?

(i) that the sum of the two numbers that turn up is 8?

(ii) of obtaining a total of 6?

(iii) of obtaining a total of 10?

(iv) of obtaining the same number on both dice?

(v) of obtaining a total more than 9?

(vi) that the sum of the two numbers appearing on the top of the dice is 13?

(vii) that the sum of the numbers appearing on the top of the dice is less that or equal to 12?

(viii) that the product of numbers appearing on the top of the two dice is 2.

(ix) that the difference of the numbers appearing on the top of the two dice is 2.

22

One card is drawn from a well shuffled deck of 52 cards. Find the probability of getting:

(i) a king of red suit

(ii) a face card

(iii) a red face card

(iv) a queen of black suit

(v) a jack of hearts

23

Five cards – ten, jack, queen, king and an ace of diamonds are shuffled face downwards. One card is picked at random.

(i) What is the probability that the card is a queen?

(ii) If a king is drawn first and put aside, what is the probability that the second card picked up is the (a) ace? (b) king?

24

A bag contains 3 red balls and 5 black balls. A ball is drawn at random form the bag. What is the probability that the ball drawn is:

(i) red

(ii) black

25

A bag contains cards which are numbered from 2 to 90. A card is drawn at random from the bag. Find the probability that it bears

(i) a two digit number

(ii) a number which is a perfect square

26

A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the number 1, 2, 3,…, 12 as shown in Fig. 13.3. What is the probability that it will point to:

(i) 10?

(ii) an odd number?

(iii) a number which is multiple of 3?

(iv) an even number?

27

Two customers are visiting a particular shop in the same wee (Monday to Saturday). Each is equally likely to visit the shop on any one day as on another. What is the probability that both will visit the shop on:

(i) the same day?

(ii) different days?

(iii) consecutive days?

28

In a class, there are 18 girls and 16 boys. The class teacher wants to choose one pupil for class monitor. What she does, she writes the name of each pupil on a card and puts then into a basket and mixes thoroughly. A child is asked to pick one card from the basket. What is the probability that the name written on the card is:

(i) the name of a girl

(ii) the name of a boy

29

Why is tossing a coin considered to be a fair way of deciding which team should choose ends in a game of cricket?

30

What is the probability that a number selected at random from the number 1, 2, 2, 3, 3, 3, 4, 4, 4, 4 will be their average?

31

The faces of a red cube and a yellow cube are numbered from 1 to 6. Both cubes are rolled. What is the probability that the top face of each cube will have the same number?

32

The probability of selecting a green marble at random form a jar that contains only green, white and yellow marbles is 1/4. The probability of selecting a white marble at random form the same jar is 1/3. If this jar contains 10 yellow marbles. What is the total number of marbles in the jar?

33

There are 30 cards, of same size, in a bag on which 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.

34

A bag contains 5 red, 8 white and 7 black balls. A ball is drawn at random from the bag. Find the probability that the drawn ball is (i) red or white (ii) not black (iii) neither white nor black.

35

Find the probability that a number selected from the number 1 to 25 is not a prime number when each of the given numbers is equally likely to be selected.

36

A bag contains 8 red, 6 white and 4 black balls. A ball is drawn at random from the bag. Find the probability that the drawn ball is

(i) red or white

(ii) not black

(iii) neither white or black

37

Find the probability that a number selected at random from the numbers 1, 2, 3,…, 35 is a

(i) prime number

(ii) multiple of 7

(iii) a multiple of 3 or 5

38

From a pack of 52 playing cards Jacks, queens, kings and aces of red colour are removed. From the remaining, a card is drawn at random. Find the probability that the card drawn is

(i) a black queen

(ii) a red card

(iii) a black jack

(iv) a picture card (Jacks, queens and kings are picture cards).

39

A bag contains lemon flavoured candies only. Malini takes out one candy without looking into the bag. What is the probability that she takes out.

(i) an orange flavoured candy?

(ii) a lemon flavoured candy?

40

It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?

41

A bag contains 3 red balls and 5 black balls is drawn at random from the bag. What is the probability that the ball drawn is (i) red? (ii) not red?

42

A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be (i) red (ii) white (iii) not green

43

(i) A lot of 20 bulbs contain 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective?

(ii) Suppose the bulb drawn in (i) is not defective and not replaced. Now bulb is drawn at random from the box, find the probability that it bears (i) a two digit number (ii) a perfect square number (ii) a number divisible by 5.

44

A box contains 90 discs which are numbered from 1 to 90. If one discs is drawn at random from the box, find the probability that it bears (i) a two digit number (ii) a perfect square number (iii) a number divisible by 5.

45

A lot consists of 144 ball pens of which 20 are defective and others 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

(ii) She will not buy it?

46

12 defective pens are accidently mixed with 132 good ones. It is not possible to just look at pen and tell whether or not it is defective. One pen is taken out at random from this lit. Determine the probability that the pen taken out is good one.

47

Five cards – the ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random.

(i) What is the probability that the card is the queen?

(ii) If the queen is drawn and put a side, what is the probability that the second card picked up is (a) an ace? (b) a queen?

48

Harpreet tosses two different coins simultaneously (say, one is of Re 1 and other of Rs 2). What is the probability that he gets at least one head?

49

Two dice, one blue and one grey, are thrown at the same time. Complete the following table:

 Events: 2 3 4 5 6 7 8 9 10 11 12 Sum on two dice' Probability

From the above table a student argues that there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability . Do you agree with this argument?

50

Cards marked with numbers 13, 14, 15, …, 60 are placed in a box and mixed thoroughly. One card is drawn at random from the box. Find the probability that number on the card drawn is

(i) divisible by 5

(ii) a number is a perfect square

51

A bag contains 6 red balls and some blue balls. If the probability of drawing a blue ball from the bag is twice that of a red ball, find the number of blue balls in the bag.

52

A bag contains tickets numbered 11, 12, 13, …, 30. A tickedt is taken out from the bag at random. Find the probability that the number on the drawn ticket (i) is a multiple of 7

(ii) is greater than 15 and a multiple of 5.

53

The king, queen and jack of clubs are removed from a deck of 52 playing cards and the remaining cards are shuffled. A card is drawn from the remaining cards. Find the probability of getting a card of (i) heart (ii) queen

(iii) clubs.

54

Two dice are thrown simultaneously. What is the probability that:

(i) 5 will not come up on either of them?

(ii) 5 will come up on at least one?

(iii) 5 will come up at both dice?

55

Fill in the blanks:

(i) Probability of a sure event is ………. .

(ii) Probability of an impossible event is ………….. .

(iii) The probability of an event (other than sure and impossible event) lies between ……….. .

(iv) Every elementary event associated to a random experiment has ………. Probability.

(v) Probability of an event A+ Probability of event ‘not A’ = ………….. .

(vi) Sum of the probabilities of each outcome in an experiment is …………. .

56

Examine each of the following statements and comment:

(i) If two coins are tossed at the same time, there are 3 possible outcomes – two heads, two tails, or one of each. Therefore, for each outcome, the probability of occurrence is 1/3.

(ii) If a die is thrown once, there are two possible outcomes – an odd number or an even number. Therefore, the probability of obtaining an odd number is � and the probability of obtaining an even number is 1/2.

57

A box contains 100 red cards, 200 yellow cards and 50 blue cards. If a card is drawn at random from the box, then find the probability that it will be (i) a blue card (ii) not a yellow card (iii) neither yellow nor a blue card

58

A number is selected at random from first 50 natural numbers. Find the probability that it is a multiple of 3 and 4.

59

A box contains cards numbered 3, 5, 7, 9, …, 35, 37. A card is drawn at random from the box. Find the probability that the number on the drawn card is a prime number.

60

A group consists of 12 persons, of which 3 are extremely patient, other 6 are extremely honest and rest are extremely kind. A person from the group is selected at random. Assuming that each person is equally likely to be selected, find the probability of selecting a person who is (i) extremely patient (ii) extremely kind or honest. Which of the above you prefer more.

61

Cards numbered 1 to 30 are put in a bag. A card is drawn at random from this bag. Find the probability that the number on the drawn card is

(i) not divisible by 3

(ii) a prime number greater than 7

(iii) not a perfect square number.

62

A dice is rolled twice. Find the probability that

(i) 5 will not come up either time.

(ii) 5 will come up exactly one time

63

A piggy bank contains hundred 50 paise coins, fifty ` 1 coins, twenty ` 2 coins and ten ` 5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, find the probability that the coin which fell

(i) will be a 50 paise win

(ii) will be of value more than ` 1

(iii) will be of value less than ` 5

(iv) will be a ` 1 or ` 2 coin

64

All the black face cards are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is drawn at random. Find the probability of getting a

(i) face card (ii) red card

(iii) black card (iv) king.

65

Cards numbered from 11 to 60 are kept in a box. If a card is drawn at random from the box, find the probability that the number on the drawn cards is

(i) an odd number

(ii) a perfect square number

(iii) divisible by 5

(iv) a prime number less than 20

66

A bag contains cards numbered from 1 to 49. A card is drawn from the bag at random, after mixing the card thoroughly. Find the probability that the number on the drawn card is

(i) an odd number

(ii) a multiple of 5

(iii) a perfect square

(iv) an even prime number.

67

All kings and queens are removed from a pack of 52 cards. The remaining cards are well – shuffled and then a card is randomly drawn from it. Find the probability that this card is (i) a red face card (ii) a black card.

68

All jacks, queens and kings are removed from a pack of 52 playing cards. The remaining cards are well – shuffled and then a card is randomly drawn from it. Find the probability that this card is

(i) a black face card (ii) a red card

69

Red queens and black jacks are removed from a pack of 52 playing cards. A cards is drawn at random from the remaining cards, after reshuffling them. Find the probability that the card drawn is

(i) a king (ii) of red colour

(iii) a face card (iv) a queen

70

A box contains 20 cards numbered from a 1 to 20. A card is drawn at random form the box. Find the probability that the number on the drawn card is

(i) divisible by 2 or 3

(ii) a prime number

71

In a bag there are 44 identical cards with figure of circles, of which 9 are blue and rest are green and 20 squares of which 11 are blue and rest are green. One card is drawn from the bag at random. Find the probability that it has the figure of (i) square (ii) green colour (iii) blue circle and (iv) green square.

72

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 and (iii) a card of clubs.

## CCE - Formative Assessment

1

Cards each marked with one of the numbers 4, 5, 6, ..., 20 are placed in a box and mixed thoroughly. One card is drawn at random from the box. What is the probability of getting an even number?

2

One card is drawn from a well shuffled deck of 52 playing cards. What is the probability of getting a non-face card?

3

A bag contains 5 red, 8 green and 7 white balls. One ball is drawn at random from the bag. What is the probability of getting a white ball or a green ball?

4

A die is thrown once. What is the probability of getting a prime number?

5

A die is thrown once. What is the probability of getting a number lying between 2 and 6?

6

A die is thrown once. What is the probability of getting an odd number?

7

If E denote the complement or negation of an even E, what is the value of ?

8

One card is drawn at random from a well shuffled deck of 52 cards. What is the probability of getting an ace?

9

Two coins are tossed simultaneously. What is the probability of getting at least one head?

10

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn bears a number which is a multiple of 3?

11

From a well shuffled pack of cards, a card is drawn at random. Find the probability of getting a black queen.

12

A die is thrown once. Find the probability of getting a number less than 3.

13

Two coins are tossed simultaneously. Find the probability of getting exactly one head.

14

A die is thrown once. What is the probability of getting a number greater than 4?

15

What is the probability that a number selected at random from the numbers 3, 4, 5, ..., 9 is a multiple of 4?

16

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

1

If a digit is chosen at random from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, then the probability that it is odd, is

2

In Q. No. 1, the probability that the digit is even, is

3

In Q. No. 1, the probability that the digit is a multiple of 3 is

4

If three coins are tossed simultaneously, then the probability of getting at least two heads, is

5

In a single throw of a die, the probability of getting a multiple of 3 is

6

A number x is chosen at random from the numbers -3, -2, -1, 0, 1, 2, 3 the probability that |x| < 2 is

7

The probability of guessing the correct answer to a certain test questions is x/12 . If the probability of not guessing the correct answer to this question is 2/3, then x =

8

A bag contains three green marbles, four blue marbles, and two orange marbles. If a marble is picked at random, then the probability that it is not an orange marble is

9

A number is selected at random from the numbers 3, 5, 5, 7, 7, 7, 9, 9, 9, 9 The probability that the selected number is their average is

10

If a number x is chosen from the numbers 1, 2, 3, and a number y is selected from the numbers 1, 4, 9. Then, P (xy < 9)

11

The probability of throwing a number greater than 2 with a fair dice is

12

A card is accidently dropped from a pack of 52 playing cards. The probability that it is an ace is

13

The probability that a non-leap year has 53 sundays, is

14

A number is selected from numbers 1 to 25. The probability that it is prime is

15

In a single throw of a pair of dice, the probability of getting the sum a perfect square is

16

Which of the following cannot be the probability of an event?

17

If P(E) = 0.05, then P(not E) =

18

Which of the following cannot be the probability of occurrence of an event?

19

The probability of a certain event is

20

The probability of an impossible event is

21

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

22

Aarushi sold 100 lottery tickets in which 5 tickets carry prizes. If Priya purchased a ticket, what is the probability of Priya winning a prize?

23

A number is selected from first 50 natural numbers. What is the probability that it is a multiple of 3 or 5?

24

Two numbers 'a' and 'b' are selected successively without replacement in that order from the integers 1 to 10. The probability that a/b is an integer, is

25

Two dice are rolled simultaneously. The probability that they show different faces is

26

What is the probability that a leap year has 52 Mondays?

27

A month is selected at random in a year. The probability that it is March or October, is

28

From the letters of the word "MOBILE", a letter is selected. The probability that the letter is a vowel, is

29

If a two digit number is chosen at random, then the probability that the number chosen is a multiple of 3, is

30

Two dice are thrown together. The probability of getting the same number on both dice is

31

A die is thrown once. The probebility of getting a prime number is

32

The probability of getting an even number, when a die is thrown once is

33

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

34

The probability that a number selected at random from the numbers 1, 2, 3,...,15 is a multiple of 4, is

35

In a family of 3 children, the probability of having at least one boy is

36

A bag contains cards numbered from 1 to 25. A card is drawn at random from the bag. The probability that the number on this card is divisible by both 2 and 3 is

37

Two different coins are tossed simultaneously. The probability of getting at least one head is

38

If two different dice are rolled together, the probability of getting an even number on both dice, is