Probability

Question: Two dice are tossed. The probability that the total score is a prime number is:

[A].

1

6

[B].

5

12

[C].

1

2

[D].

7

9

Answer: Option B

Explanation:

Clearly, n(S) = (6 x 6) = 36.

Let E = Event that the sum is a prime number.

Then E

= { (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3),       (5, 2), (5, 6), (6, 1), (6, 5) }

n(E) = 15.

P(E) =	n(E)	=	15	=	5	.
	n(S)		36		12

Question:
In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:

[A].

21

46

[B].

25

117

[C].

1

50

[D].

3

25

Answer: Option A

Explanation:

Let S be the sample space and E be the event of selecting 1 girl and 2 boys.

Then, n(S)	= Number ways of selecting 3 students out of 25
	= 25C3 `
	= (25 x 24 x 23) (3 x 2 x 1)
	= 2300.

n(E)	= (10C1 x 15C2)
	= 10 x (15 x 14) (2 x 1)
	= 1050.

P(E) =	n(E)	=	1050	=	21	.
	n(S)		2300		46

Question:
In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?

[A].

1

3

[B].

3

4

[C].

7

19

[D].

8

21

Answer: Option A

Explanation:

Total number of balls = (8 + 7 + 6) = 21.

Let E	= event that the ball drawn is neither red nor green
	= event that the ball drawn is blue.

n(E) = 7.

P(E) =	n(E)	=	7	=	1	.
	n(S)		21		3

Question:
A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

[A].

10

21

[B].

11

21

[C].

2

7

[D].

5

7

Answer: Option A

Explanation:

Total number of balls = (2 + 3 + 2) = 7.

Let S be the sample space.

Then, n(S)	= Number of ways of drawing 2 balls out of 7
	= 7C2 `
	= (7 x 6) (2 x 1)
	= 21.

Let E = Event of drawing 2 balls, none of which is blue.

n(E)	= Number of ways of drawing 2 balls out of (2 + 3) balls.
	= 5C2
	= (5 x 4) (2 x 1)
	= 10.

P(E) =	n(E)	=	10	.
	n(S)		21

Question:
A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:

[A].

1

22

[B].

3

22

[C].

2

91

[D].

2

77

Answer: Option C

Explanation:

Let S be the sample space.

Then, n(S)	= number of ways of drawing 3 balls out of 15
	= 15C3
	= (15 x 14 x 13) (3 x 2 x 1)
	= 455.

Let E = event of getting all the 3 red balls.

n(E) = 5C3 = 5C2 =	(5 x 4)	= 10.
	(2 x 1)

P(E) =	n(E)	=	10	=	2	.
	n(S)		455		91

Question:
A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?

[A].

3

4

[B].

4

7

[C].

1

8

[D].

3

7

Answer: Option B

Explanation:

Let number of balls = (6 + 8) = 14.

Number of white balls = 8.

P (drawing a white ball) =	8	=	4	.
	14		7

Question: Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is:

[A].

3

20

[B].

29

34

[C].

47

100

[D].

13

102

Answer: Option D

Explanation:

Let S be the sample space.

Then, n(S) = 52C2 =	(52 x 51)	= 1326.
	(2 x 1)

Let E = event of getting 1 spade and 1 heart.

n(E)	= number of ways of choosing 1 spade out of 13 and 1 heart out of 13
	= (13C1 x 13C1)
	= (13 x 13)
	= 169.

P(E) =	n(E)	=	169	=	13	.
	n(S)		1326		102

Question: From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings?
[A].

1

15

[B].

25

57

[C].

35

256

[D].

1

221

Answer: Option D

Explanation:

Let S be the sample space.

Then, n(S) = 52C2 =	(52 x 51)	= 1326.
	(2 x 1)

Let E = event of getting 2 kings out of 4.

n(E) = 4C2 =	(4 x 3)	= 6.
	(2 x 1)

P(E) =	n(E)	=	6	=	1	.
	n(S)		1326		221

Question:
A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is:

[A].

1

13

[B].

2

13

[C].

1

26

[D].

1

52

Answer: Option C

Explanation:

Here, n(S) = 52.

Let E = event of getting a queen of club or a king of heart.

Then, n(E) = 2.

P(E) =	n(E)	=	2	=	1	.
	n(S)		52		26

Question: One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen and King only)?
[A].

1

13

[B].

3

13

[C].

1

4

[D].

9

52

Answer: Option B

Explanation:

Clearly, there are 52 cards, out of which there are 12 face cards.

P (getting a face card) =	12	=	3	.
	52		13