# probability aptitude 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
m
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