In a game, 3 coins are tossed. A person is paid $₹ 100$, if he gets all heads or all tails; and he is…
In a game, 3 coins are tossed. A person is paid $₹ 100$, if he gets all heads or all tails; and he is supposed to pay ₹ 40 , if he gets one head or two heads. The amount he can expect to win/lose on an average per game in ( $₹$ ) is
10 loss
5 loss
5 gain
10 gain
Solution
In a game, 3 coins are tossed.
$\mathrm{P}($ getting all heads or all tails $)=\frac{2}{8}=\frac{1}{4}$
$\mathrm{P}($ getting one head or two heads $)=\frac{6}{8}=\frac{3}{4}$
Let $x$ : number of rupees the person gets.
$\begin{aligned}
& P(X=100)=\frac{1}{4} \\
& P(X=-40)=\frac{3}{4}
\end{aligned}$
$\therefore \quad$ The amount he can expect to win $=$ mean
$\begin{aligned}
& =\sum \mathrm{n}_{\mathrm{i}} \mathrm{p}_{\mathrm{i}} \\
& =100 \times \frac{1}{4}+(-40) \times \frac{3}{4} \\
& =\frac{100}{4}-\frac{120}{4} \\
& =-5 \\
& =5 \mathrm{loss}
\end{aligned}$