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# 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.

Given:

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.

To do:

We have to calculate the probability that Hanif will lose the game.

Solution:

The possible outcomes when a coin is tossed three times are $HHH, TTT, HHT, HTH, THH, TTH, THT, HTT$

This implies,

The total number of possible outcomes $n=8$.

The number of tosses where all the three tosses give the same result $=2$

This implies,

Number of favorable outcomes $=8-2=6$

We know that,

Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$

Therefore,

Probability that Hanif will lose the game $=\frac{6}{8}$

$=\frac{3}{4}$

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