(a) Repeat the ‘balls in the bag’ exercise from the text, but with bag A containing five red and…

(a) Repeat the ‘balls in the bag’ exercise from the text,
but with bag A containing five red and three yellow balls, bag B containing one
red and two yellow balls. The single ball drawn is red. Before doing the
calculation, predict which bag is more likely to be the source of the drawn
ball. Explain why. Then compare your prediction with the calculated answer.

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(b) Bag A now contains 10 red and 6 yellow balls (i.e. twice
as many as before, but in the same proportion). Does this alter the answer you
obtained in part (a)?

(c) Set out your answer to part (b) in the form of prior
probabilities and likelihoods, in order to obtain the posterior probability.