 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/ii/solution

Let

C_{j}

identify the selected coin and let

H

be the event of two heads. The prior coin probabilities are equal, and the conditional probabilities of

H

are

1/9, 1/4, 4/9

P (C_{1} ∣ H) = \frac{( 1/3 ) ( 1/9 )}{( 1/3 ) ( 1/9 + 1/4 + 4/9 )} = \frac{4}{29} .

The full posterior distribution over the three biases is

(4, 9, 16) /29

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