Mathematics

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.

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When one rupee coin is tossed three times.

Total possible outcomes are = {HHH, TTT, HTH, HHT, THH, THT, TTH, HTT}

∴ Number of possible outcomes = 8

∴ Number of favourable outcomes (to not get three heads or three tails) = 6.

P(Hanif will lose the game)

= $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{6}{8} = \dfrac{3}{4}$ .

Hence, the probability that Hanif will lose the game is $\dfrac{3}{4}$ .

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