MHT CET · Maths · Probability
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 ₹
- A \(-0.5\)
- B \(0.5\)
- C \(1\)
- D \(-1\)
Answer & Solution
Correct Answer
(A) \(-0.5\)
Step-by-step Solution
Detailed explanation
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
\(\begin{aligned}
& =\sum x_i \mathrm{p}_{\mathrm{i}} \\
& =7\left(\frac{1}{4}\right)+-3\left(\frac{3}{4}\right) \\
& =-0.5
\end{aligned}\)
\(\mathrm{P}(\) 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
\(\begin{aligned}
& =\sum x_i \mathrm{p}_{\mathrm{i}} \\
& =7\left(\frac{1}{4}\right)+-3\left(\frac{3}{4}\right) \\
& =-0.5
\end{aligned}\)
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