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GO Classes | IIITH PGEE 2026 | Memory Based | Question: 30

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Given:
\begin{align*}
P(F) &= \frac{3}{4}, \quad P(\text{Heads} \mid \text{Fair}) = 0.5 \\
P(B) &= \frac{1}{4}, \quad P(\text{Heads} \mid \text{Biased}) = 0.8
\end{align*}

By the Total Probability Theorem:
\begin{align*}
P(\text{Heads}) &= P(\text{Heads} \mid \text{Fair}) \times P(F) 
                 + P(\text{Heads} \mid \text{Biased}) \times P(B) \\
                &= 0.5 \times \frac{3}{4} + 0.8 \times \frac{1}{4} \\
                &= \frac{1.5}{4} + \frac{0.8}{4} \\
                &= \frac{2.3}{4} \\
                &= \boxed{0.575}
\end{align*}

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