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.

Answer 1

The outcomes associated with the experiment in which a coin is tossed thrice:
$HHH,HHT,HTH,THH,TTH,HTT,THT,TTT$
Therefore, total number of outcomes $=8$

Probability $=\frac{\text{Number of favourable outcomes}}{\text{Total umber of outcomes}}$
Number of favourable outcomes (for Hanif to lose the match) $=6$
Hence, required probability $=\frac{6}{8}=\frac{3}{4}$