Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2025 / Paper 2 / 10 / b / Solution

The successful ordered outcomes are $TTH$, $THT$ and $HTT$. Each has probability $1/8$ by independence, and these events are mutually exclusive. Adding their probabilities givesEquivalently, the binomial distribution gives $\left(\genfrac{}{}{0ex}{}{3}{2}\right)(1/2{)}^2(1/2)=3/8$.