Question

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Suppose a box contains five coins (numbered 1, 2, 3, 4 and 5) but each coin has a different probability of obtaining a head when it is tossed. Let the p_i be given by 0,1/4,1/2,3/4 and 1.0, respectively for the coins, indexed by i=1,…,5.

1. Suppose a coin is randomly chosen from the box (i.e. each coin has the same probability of being chosen) and tossed. It shows a head. What are the posterior probabilities that the coin was number i?

2. If that coin were tossed again what is the probability of obtaining another head.

3. Suppose a tail had been obtained on the first toss, and the coin were tossed again. What is the probability a head would be obtained on the second toss?

Answer 1

Solution;