In a game, 3 coins are tossed. A person is paid $₹ 7 /$, if he gets all heads or all tails; and he is…
In a game, 3 coins are tossed. A person is paid $₹ 7 /$, if he gets all heads or all tails; and he is supposed to pay $₹ 3 /-$, if he gets one head or two heads. The amount he can expect to win on an average per game is $₹$
$-0.5$
$0.5$
$1$
$-$
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 $\mathrm{X}$ : number of rupees the person gets.
$\begin{aligned}
& P(X=7)=\frac{1}{4} \\
& P(X=-3)=\frac{3}{4}
\end{aligned}$
$\therefore \quad$ The amount he can expect to win $=$ Mean
$\begin{aligned}
& =\sum x_i \mathrm{p}_{\mathrm{i}} \\
& =7\left(\frac{1}{4}\right)+-3\left(\frac{3}{4}\right) \\
& =-0.5
\end{aligned}$