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Probability ( 16 to 20 ):
APTITUDE QUESTIONS (PROBABILITY):
16. The probability that a card drawn from a pack of 52 cards will be a diamond or a king is:
A) (2/13)
B) (4/13)
C) (1/13)
D) (4/52)
E) None of these
View Answer
Answer: option (B)
Explanation:
Here, n(S) = 52
There are 13 cards of diamond (including one king) and then there are more kings.
Let E = event of getting a diamond or a king.
Then, n(E) = (13+3) = 16
∴ P(E) = (n(E)/n(S)) = (16/52) = (4/13)
17. 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)
E) None of these
View Answer
Answer: option (D)
Explanation:
Let S be the sample space. Then,
n(S) = 52C2 = ((52*51)/(2*1)) = 1326
Let E = event of getting 1 spade and 1 heart.
∴ n(E) = 4C2 = ((4*3)/(2*1)) = 6
∴ P(E) = (n(E)/n(S)) = (6/1326) = (1/221)
18. A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
A) (3/4)
B) (4/7)
C) (1/8)
D) (3/7)
E) None of these
View Answer
Answer: option (B)
Explanation:
Total number of balls = (6 + 8) = 14
Number of white balls = 8
∴ P(drawing a white ball) = (8/14) = (4/7)
19. In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
A) (2/3)
B) (3/4)
C) (7/19)
D) (8/21)
E) None of these
View Answer
Answer: option (D)
Explanation:
Total number of balls = (8 + 7 + 6) = 21
Let E = event that the ball drawn is neither red nor green
= event that the ball drawn is red
∴ n(E) = 8
∴ P(E) = (8/21)
20. Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is:
A) (3/20)
B) (29/34)
C) (47/100)
D) (13/102)
E) None of these
View Answer
Answer: option (D)
Explanation:
Let S be the sample space. Then,
n(S) = 52C2 = ((52*51)/(2*1)) = 1326
Let E = event of getting 1 spade and 1 heart.
∴ n(E) = number of ways of choosing 1 spade out of 13 and 1 heart out of 13
= (13C1 * 13C1) = (13 * 13) = 169
∴ P(E) = (n(E)/n(S)) = (169/1326) = (13/102)