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

Let's find the probability of lose of game by Hanif.

We know that the probability of event to happen $P\left(E\right)=\frac{Numberoffavorableoutcomes}{TotalNumberofoutcomes}$

The total possible outcomes on tossing the $3$ coins are listed below

$\left\{HHH,TTT,HTH,HHT,THH,THT,HTT\right\}=8$

The number of possible outcomes to get three heads or three tails $=2$

The probability that Hanif will win the game

$$\begin{gathered} =\frac{Numberofpossibleoutcomes}{TotalNumberoffavourableoutcomes} \\ =\frac{2}{8}=\frac{1}{4} \end{gathered}$$

The probability that Hanif will lose the game is $=1-\frac{1}{4}=\frac{3}{4}$

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