Quantitative Aptitude Questions and Answers - Probability
11. A carton contains 12 green and 8 blue bulbs .2 bulbs are drawn at random. Find the probability that they
are of same colour?
A. (91/47)
B. (47/105)
C. (47/95)
D. (47/145)
View Answer
Ans : C
Explanation: Let S be the sample space
Then n(S) = no of ways of drawing 2 bulbs out of (12+8) = 20c2=20*19/2*1=190
Let E = event of getting both bulbs of same colour
Then, n(E) = no of ways (2 bulbs out of 12) or (2 bulbs out of 8)
=12C2+ 8C2=(132/2)+(56/2) = 66+28 = 94
Therefore, P(E) = n(E)/n(S) = 94/190 = 47/95
12. In a Coupon, there are 30prizes and 75blanks. A Coupon is drawn at random. What is the probability of
getting a prize?
A. (2/7)
B. (5/7)
C. (1/2)
D. (5/12)
View Answer
Ans : A
Explanation: Total number of outcomes possible, n(S) = 30+75 = 105
Total number of prizes, n(E) = 30
P(E)=n(E)/n(S)=30/105=2/7
13. Two dice are rolling simultaneously .What is the probability that the sum of the number on the two faces is
divided by 5 Or 7
A. (13/36)
B. (14/36)
C. (15/36)
D. (11/36)
View Answer
Ans : D
Explanation: Clearly, n(S) = 6 x 6 = 36
Let E be the event that the sum of the numbers on the two faces is divided by 5or 7.
Then,E = {(1,4),(1,6),(2,3),(2,5),(3,2),(3,4),(4,1),(4,3),(4,6),(5,2),(5,5),(6,1),(6,4)}
n(E) = 11.
Hence, P(E) = n(E)/n(S) = 11/36
14. Consider a pack contains 2black, 9 white and 3 pink pencils. If a pencil is drawn at random from the pack,
replaced and the process repeated 2 more times, What is the probability of drawing 2 black pencils and 1 pink
pencil?
A. (3/49)
B. (3/386)
C. (3/14)
D. (3/545)
View Answer
Ans : B
Explanation: Here, total number of pencils = 14
Probability of drawing 1 black pencil = 2/14
Probability of drawing another black pencil = 2/14
Probability of drawing 1 pink pencil = 3/14
Probability of drawing 2 black pencils and 1 pink pencil = 2/14 * 2/14 * 3/14 = 3/686
15. A box contains 3red, 8 blue and 5 green marker pens. If 2 marker pens are drawn at random from the
pack, not replaced and then another pen is drawn. What is the probability of drawing 2 blue marker pens and
1 red marker pen?
A. (1/20)
B. (3/20)
C. (7/20)
D. (9/20)
View Answer
Ans : A
Explanation: Probability of drawing 1 blue marker pen =8/16
Probability of drawing another blue marker pen = 7/15
Probability of drawing 1 red marker pen = 3/14
Probability of drawing 2 blue marker pens and 1 red marker pen = 8/16*7/15*3/14=1/20
16. Consider the example of finding the probability of selecting a red card or a 9 from a deck of 52 cards
A. (5/13)
B. (6/13)
C. (7/13)
D. (8/13)
View Answer
Ans : C
Explanation: Probability of selecting a Red card = 26/52
Probability of selecting a 9 = 4/52
Probability of selecting both a red card and a 9 = 2/52
P(R or 9) = P(R) + P(9) – P(R and 9)
= 26/52 + 4/52 – 2/52
= 28/52
= 7/13
17. A single coin is tossed 7 times. What is the probability of getting at least one tail?
A. (55/128)
B. (56/128)
C. (127/128)
D. (126/128)
View Answer
Ans : C
Explanation: Consider solving this using complement.
Probability of getting no tail = P(all heads) = 1/128
P(at least one tail) = 1 – P(all heads) = 1 – 1/128 = 127/128
18. Murali and his wife appear in an interview for two vacancies in the same post. The probability of murali's
selection is (1/6) and the probability of wife's selection is (1/4). What is the probability that only one of them is
selected ?
A. (1/2)
B. (1/3)
C. (1/4)
D. (1/6)
View Answer
Ans : B
Explanation: A= Event that the husband is selected
B =Event that the wife is selected
P(A)=1/6,P(B)=1/4
P(Ac)=1-1/6=5/6
P(Bc)=1-1/4=3/4
Required Probability=P[ (A and notB) or(B and not A)]
= P(A). P(Bc) + P(B) P(Ac)
=1/6*3/4 + 1/4 * 5/6 = 1/3
19. Two dice are tossed. The probability that the total score is a prime number is:
A. (5/12)
B. (7/12)
C. (11/12)
D. (1/3)
View Answer
Ans : A
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)/n(S)=15/36=>5/12
20. A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is:
A. (1/13)
B. (1/26)
C. (3/52)
D. (1/52)
View Answer
Ans : B
Explanation: Here, n(S) = 52.
Let E = event of getting a queen of club or a king of heart.
Then, n(E) = 2.
P(E) = n(E)/n(S)=2/52=>1/26
Discussion