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Ann has a biased coin that has a 3/5 probability of coming up heads (H) and a 2/5 probability coming up tails (T). She intends to flip it five times. You win if you correctly predict the sequence of coin flips. Suppose everyone knows that the coin flips are independent.
(a) Show that you would be more likely to win if you predicted that the sequence of coin flips is HHHHH rather than HTHHT?
(b) Explain why many people might think that they have a better chance of winning by betting on the sequence HTHHT rather than the sequence HHHHH.
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Suppose she is going to take a test with 12 multiple-choice questions. Each question has 4 possible answers, only one of which is correct.
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