 Solution

ID: 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

TT H

T H T

and

H TT

. Each has probability

1/8

P (exactly two tails) = \frac{3}{8} .

Equivalently, the binomial distribution gives

(2 3) (1/2)^{2} (1/2) = 3/8

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