Let \(X\) be a random variable such that \(X(x)\) is the number of heads in \(X\) for each \(x \in…
Let \(X\) be a random variable such that \(X(x)\) is the number of heads in \(X\) for each \(x \in \mathbf{S}\), where \(S\) is the sample space of random experiment of tossing three fair coins simultaneously. Find the value of \(\rho\left(X^{-1}(2)\right)\).
\(\frac{3}{8}\)
\(\frac{5}{8}\)
\(\frac{1}{8}\)
\(\frac{3}{4}\)
Solution
Tossing of three coins
So, \(\rho\left(X^{-1}(2)\right)\) means probability of getting two tails when three coins are tossed.
\(\Rightarrow \quad \rho\left(X^{-1}(2)\right)=\frac{3}{8}\)