Question

Three unbiased coins are tossed once. Find the probability of getting (i) exactly 2 tails (ii) exactly one tail (iii) at most 2 tails (iv) at least 2 tails (v) at most 2 tails or at least 2 heads Select the correct answer from above options

Answer 1

When 3 unbiased coins are tossed once, then possible outcomes are: TTT, TTH, THT, HTT, THH, HTH, HHT, HHH Total number of outcomes = 8 We know, Probability of occurrence of an event = (Total number of favorable outcomes) / (Total number of outcomes) (i) exactly 2 tails Possible outcomes: TTH, THT, HTT Total number of outcomes = 3 Therefore, the probability of getting exactly 2 tails = 3/8 (ii) exactly one tail Possible outcomes: THH, HTH, HHT Total number of outcomes = 3 Therefore, the probability of getting exactly one tail = 3/8 (iii) at most 2 tails Possible outcomes: THH, HTH, HHT, TTH, THT, HTT, HHH Total number of outcomes = 7 Therefore, the probability of getting at most 2 tails = 7/8 (iv) at least 2 tails Possible outcomes: TTH, THT, HTT, TTT Total number of outcomes = 4 Therefore, the probability of getting at least 2 tails = 4/8 = 1/2 (v) at most 2 tails or at least 2 heads Possible outcomes: TTH, THT, HTT, THH, HTH, HHT, HHH Total number of outcomes = 7 Therefore, the probability of getting at most 2 tails or at least 2 heads = 7/8