need help with parts C and D. I got A and B. Exercise 2.71 As in Example 2.38, a

Question

need help with parts C and D. I got A and B.

Exercise 2.71 As in Example 2.38, assume that 90% of the coins in circulation are fair, and the remaining 10% are biased coins that give tails with probability 3/5. I holda randomly chosen coin and begin to flip it. (a) After one flip that results in tails, what is the probability that the coin I hold is a biased coin? After two flips that both give tails? After n flips that all come out tails? After how many straight tails can we say that with 90% probabilitv the coin I hold is biased? (b) (c) After n straight tails, what is the probability that the next flip is also tails? (d) Suppose we have flipped a verv large number of times (think number of flips n tending to infinity), and each time gotten tails. What are the chances that the next flip again yields tails?

Explanation / Answer

Each flipping of coin is independent of the other.

Thus, getting tails or heads in the previous flips does not have any effect on the next flip.

Now, probability of getting tails = P(baised) * 3/5 + P(unbiased) * 1/2 = 0.1*3/5 + 0.9*1/2 = 0.51

Thus, in both the options (c) and (d), there are 0.51 or 51% chance that the next flip yields tails

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