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 $\rho\left(X^{-1}(2)\right)$.

Question

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 $\rho\left(X^{-1}(2)\right)$., $\frac{3}{8}$, $\frac{5}{8}$, $\frac{1}{8}$, $\frac{3}{4}$

MARKS App · Accepted Answer

Tossing of three coins So, $\rho\left(X^{-1}(2)\right)$ means probability of getting two tails when three coins are tossed. $\Rightarrow \quad \rho\left(X^{-1}(2)\right)=\frac{3}{8}$

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