Probability Problems with Solutions

Question no. 1

Six playing cards are lying face down on a table, where two of them are kings. Two cards are drawn at random. Let a denote the probability that at least one or the cards drawn is king, and b denotes the probability of not drawing a king. The ratio a/b is:
(a) ≥ 0.25 and < 0.5
(b) ≥ 0.5 and < 0.75
(c) ≥ 0.75 and < 1.0

(d) ≥1.0 and < 1.25
(e) ≥ 1.25

Question no. 2

You enter a chess tournament where your probability of winning a game is 0.3 against half the players (call them Type 1), 0.4 against a quarter of the players (call them Type 2) and 0.5 against the remaining quarter of the players (call them Type 3), You play a game against a randomly chosen opponent. What is the probability of winning the tournament?
(a) 0.365
(b) 0.452
(c) 0.375
(d) 0.236

(e) None of the above

Question no. 3

Ashish studies late in the night and is hungry. He opens his mother's snack cupboard without switching on the lights, knowing that his mother has kept 10 packets of chips and biscuits in the cupboard. He pulls out 3 packets from the cupboard and all of them turn out to be chips. What is the probability that the snack cupboard contains 1 packet of biscuits and 9 packets of chips?
(a) 6/55

(b) 12/73
(c) 14/55
(d) 7/50

(e) None of the above

Question no. 4

The answer sheets of 5 engineering students can be checked by any one of 9 professors. What is the probability that all the 5 answer sheets are checked by exactly 2 professors?
(a) 20/2187
(b) 40/2187
(c) 40/729

(d) 20/729
(e) None of the above

Question no. 5

The probability that in a household, LPG will last 60 days or more is 0.8 and that it will last
at most 90 days is 0.6. The probability that the LPG will last 60 to 90 days is:
(a) 0.40
(b) 0.50
(c) 0.75

(d) 0.80
(e) None of the above