Question

A game consist of tossing a one-rupee coin 3 times and noting the outcome each time. Ramesh will win the game if all the tosses show the same result, (i.e. either all thee heads or all three tails) and loses the game otherwise. Find the probability that Ramesh will lose the game.

Answer 1

Elementary outcomes of tossing a one-rupee coin three times are as follows:

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

∴ Total number of outcomes = 8

Ramesh will lose the game if the outcome is any of the following:

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

∴ Number of favourable outcomes = 6

Now,

Probability that Ramesh will lose the game

=\[\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}\]

=\[\frac{6}{8} = \frac{3}{4}\]

Hence, the probability that Ramesh will lose the game is\[\frac{3}{4}\]