ExamAdept

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: B

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

Number of white balls = 8.

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

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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: B

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

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

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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: D

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

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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: C

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

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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: C

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

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Questions for: Probability