Question Of The Day

Imagine a game played by five people in which each flips a coin at the same time. If all but one coin comes up the same, then the odd person wins (for example, if there are four heads and a tail then the “tail” wins). If such a situation does not occur, then the players flip again. What is the probability that the game is settled on the second toss?

a) 25/128

b) 55/256

c) 45/256

d) ¼

Ans: b) 55/256

A win occurs if there are either 4 heads and 1 tail of 1 head and 4 tails. This can take place in (5!/4!)× 2 = 10 ways.
Probability of a win = 10/25 = 5/16 ∴ required probability = (11/16) 5 (5/16) = 55/256