 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ia/paper-2/12f/c/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

\sum_{n} P (A_{n}) = \infty

, part (b) gives

0 \leq E [2^{- N}] \leq e^{- \infty} = 0.

Thus

2^{- N} = 0

almost surely. By the convention in the question, this occurs exactly when

N = \infty

. Therefore

P (N = \infty) = 1 .

 New to topics? Read the docs here!