A game consists of tossing a one-rupee coin three times, and noting its outcome each time. If getting the same result in all the tosses is a success, find the probability of losing the game.

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Solution

When a coin is tossed three times, the possible outcomes are

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

Total number of outcomes = 8

A game can be lost if the if all the tosses do not give the same result. The outcomes where tosses do not give the same result are

HHT, HTH, THH, HTT, THT, TTH

Favourable number of outcomes for losing the game = 6

∴ P(Game is lost) = $\frac{Favourable number of outcomes for losing the game}{Total number of outcomes} = \frac{6}{8} = \frac{3}{4}$

Thus, the probability of losing the game is $\frac{3}{4}$ .

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