# Aptitude - Probability

### Exercise :: Probability - General Questions

6.

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

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

7.

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

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

8.

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

Explanation:

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

9.

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

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

10.

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

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