 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2014/discrete-mathematics-continuous-mathematics-and-probability/7/b/iii/solution

Given the coin, the next toss is independent of its earlier tosses and has that coin's head probability. Averaging using the posterior distribution gives the posterior predictive probability

P (next head ∣ H) = \frac{4}{29} \frac{1}{3} + \frac{9}{29} \frac{1}{2} + \frac{16}{29} \frac{2}{3} = \frac{33}{58} .

Observing two heads raises the probability of having chosen a high-bias coin.

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