Probability

Question:
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

Question: 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

Question:
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

Question: 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

Question:
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