Question

A game consists of tossing a one-rupee coin three times and noting its outcome each time. Hanif wins if all the tosses give the same result, i.e., three heads or three tails and loses otherwise. Calculate the probability that Hanif will lose the game.

Answer 1

In tossing a one-rupee coin three times, all possible outcomes are HHH, HHT, HTH, HTT, TTH, TTT.
Total number of all possible outcomes = 8.
Let E be the evnet of getting 3 heads or 3 tails.
Then, E consists of HHH, TTT.
Number of favourable outcomes of E = 2.
P(that Hanif wins the game) = P (getting 3 heads 3 tails)
` = P(E) = 2/8 = 1/4`.
P(that Hanif loses the game) = `1-P(E ) = (1-1/4) = 3/4`.