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
Answer & Explanation
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
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
Answer & Explanation
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
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
Answer & Explanation
Answer: Option C
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
Answer & Explanation
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
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
Answer & Explanation
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