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Tricky Questions on Probability
Probability - Aptitude
11.Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?
x
Option: B
Explanation
n(S) = (6 * 6) = 36
E = event of getting two numbers whose product is even
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, 5), (5, 2), (5, 4), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6))
P(E) = n(E)/n(S) = 27/36 = 3/4
12.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:
x
Option: C
Explanation
n(S) = number of ways of selecting 3 students out of 25
n(S) = 25C3 = (25 * 24 * 23)/(3 * 2 * 1) = 2300
n(E) = 10C1 * 15C2 = 10 * ((15 * 14)/(2 * 1)) = 1050
P(E) = n(E)/n(S) = 1050/2300 = 21/46
13.From a pack of 52 cards,two cards are drawn together at random.What is the probability of both the cards being kings?
x
Option: D
Explanation
n(S) = 52C2 = (52 * 51)/(2 * 1) = 1326
E = event of getting 2 kings out of 4
n(E) = 4C2 = (4 * 3)/(2 * 1) = 6
P(E) = n(E)/n(S) = 6/1326 = 1/221
14.Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is:
x
Option: B
Explanation
n(S) = 52C2 = (52 * 51)/(2 * 1) = 1326
n(E) = number of ways of choosing 1 spade out of 13 and 1 heart out of 13
n(E) = 13C1 * 13C1 = 13 * 13 = 169
P(E) = n(E)/n(S) = 169/1326 = 13/102
15.A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red is:
x
Option: C
Explanation
n(S) = number of ways of drawing 3 balls out of 15
n(S) = 15C3 = (15 * 14 * 13)/(3 * 2 * 1) = 455
n(E) = event of getting all the 3 red balls
n(E) = 5C3 = 5C2 = (5 * 4)/(2 * 1) = 10
P(E) = n(E)/n(S) = 10/455 = 2/91
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