One of two coins is selected at random and tossed three times.
The first coin comes up heads with probability p1 = 1/3 and the
second coin with probability p2 = 2/3. a) What is the probability
that the number of heads is k? [10P] b) Find the probability that
coin 1 was tossed given that k heads were observed, for k = 0, 1,
2, 3. [15P] c) In part b, which coin is more probable when k heads
have been observed? [10P] d) Find a threshold value T such that
when k > T heads are observed, coin 1 is more probable, and when
k < T are observed, coin 2 is more probable by generalizing the
solution in part b to the case where the selected coin is tossed m
times. [15P]