A game consists of tossing a one rupee coin 3 times and noting its outcome each time.
Question:

A game consists of tossing a one rupee coin 3 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.

Solution:

The possible outcomes are

{HHH, TTT, HHT, HTH, THH, TTH, THT, HTT}

Number of total possible outcomes = 8

Number of favourable outcomes = 2 {i.e., TTT and HHH}

$P$ (Hanif will win the game) $=\frac{2}{8}=\frac{1}{4}$

$\mathrm{P}$ (Hanif will lose the game) $=1-\frac{1}{4}=\frac{3}{4}$