Expert answer:Applied Math Statistics/Probability exercises

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20. A box contains 5 coins and each has a different probability of showing heads. Let PI, .. . ,
P5 denote the probability of heads on each coin. Suppose that PI = 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 IP'(CiIH) for i = 1, … ,5.
(b) Toss the coin again. What is the probability of another head? In other words find IP'(H2IHd
where Hj = “heads on toss j.” Now suppose that the experiment was carried out as follows: We
select a coin at random and toss it until a head is obtained.
(c) Find IP'(Ci IB4) where B4 = “first head is obtained on toss 4.”
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