Sameer has two coins: one fair coin and one biased coin which lands heads with probability 3/4. He picks one coin at random (50-50) and flips it repeatedly until he gets a tails. Given that he observes 3 heads before the first tails, find the posterior probability that he picked each coin. (a) What are the prior and posterior odds for the fair coin? (b) What are the prior and posterior predictive probabilities of heads on the next flip? Here prior predictive means prior to considering the data of the first four flips.

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Sameer has two coins: one fair coin and one biased coin which lands heads with
probability 3/4. He picks one coin at random (50-50) and flips it repeatedly until he gets
a tails. Given that he observes 3 heads before the first tails, find the posterior probability
that he picked each coin.
(a) What are the prior and posterior odds for the fair coin?
(b) What are the prior and posterior predictive probabilities of heads on the next flip?
Here prior predictive means prior to considering the data of the first four flips.

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