Probability - General Questions (1)

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

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

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

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

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

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

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

In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?

A.	1/10
B.	2/5
C.	2/7
D.	5/7

Answer: Option C

Explanation:

P (getting a prize) =	10	=	10	=	2	.
	(10 + 25)		35		7

Probability - General Questions (1)

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