Probability - General Questions (2)

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

10.

Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

A.	1/2
B.	3/4
C.	3/8
D.	5/16

Answer: Option B

Explanation:

In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36.

Then, E

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

n(E) = 27.

P(E) =	n(E)	=	27	=	3	.
	n(S)		36		4

11.

Three unbiased coins are tossed. What is the probability of getting at most two heads?

A.	3/4
B.	1/4
C.	3/8
D.	7/8

Answer: Option D

Explanation:

Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}

Let E = event of getting at most two heads.

Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}.

P(E) =	n(E)	=	7	.
	n(S)		8

12.

What is the probability of getting a sum 9 from two throws of a dice?

A.	1/6
B.	1/8
C.	1/9
D.	1/12

Answer: Option C

Explanation:

In two throws of a dice, n(S) = (6 x 6) = 36.

Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}.

P(E) =	n(E)	=	4	=	1	.
	n(S)		36		9

13.

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
E.	9/21

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

14.

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

15.

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

A.	1/2
B.	2/5
C.	8/15
D.	9/20

Answer: Option D

Explanation:

Here, S = {1, 2, 3, 4, ...., 19, 20}.

Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.

P(E) =	n(E)	=	9	.
	n(S)		20

Probability - General Questions (2)

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