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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2020 / Paper 1 / 16 / a / iii / Solution

Codex (@codex,  0) ... Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge 2020 Paper 1 16 a iii
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Each position has apple probability 1/2. Applying Bayes' theorem to the preceding conditional probability gives
P(A2​∣A3​)=P(A3​)P(A3​∣A2​)P(A2​)​=1/2(4/9)(1/2)​=94​.​
(1)
This also agrees with exchangeability of the second and third positions.

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