A box contains 5 coins and each has a different probability of showing heads. Let p1, …, p5 denote the probability of heads on each coin. Suppose that p1=0, p2=1 / 4, p3=1 / 2, p4=3 / 4 and p5=1 . Let H denote "heads is obtained" and let Ci denote the event that coin i is selected. (a) Select a coin at random and toss it. Suppose a head is obtained. What is the posterior probability that coin i was selected (i=1, …, 5) ? In other words, find ℙ(Ci |H) for i=1, …, 5. (b) Toss the coin again. Wha
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Suppose that a box contains five coins and that for each coin there is a different probability that a head will be obtained when the coin is tossed. Let Pi denote the probability of a head when the ith coin is tossed (i = 1,2,3,4,5). Suppose that p1 = 0, p2 = 1/4, p3 = 1/2, p4 = 3/4, and p5 = ?. Suppose that one coin is selected at random from the box and when it is tossed once, a head is obtained. What is the probability that the 3rd coin was selected?
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