 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2018/paper-2/14/a/i/solution

Distinguish the production type as well as the stopping position. The sample space has the six outcomes

Ω = {G \cap x_{0}, G \cap x_{1}, G \cap x_{2}, D \cap x_{0}, D \cap x_{1}, D \cap x_{2}} .

Here

x_{k}

X = x_{k}

. Their joint probabilities are

p g_{k}

and

(1 - p) d_{k}

, respectively. The conditional stopping laws obey

\sum_{k = 0}^{2} g_{k} = \sum_{k = 0}^{2} d_{k} = 1

; with the stated strict positivity all six outcomes are possible.

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