1) Let A and B be two events.
a) If the events A and B are mutually exclusive, are A and B always independent? If the answer is no, can they ever be independent? Explain
b) If A is a subset of B, can A and B ever be independent events? Explain
2) Flip an unbiased coin five independent times. Compute the probability of
d) Three heads occurring in the five trials.
3)An urn contains two red balls and four white balls. Sample successively five times at random and with replacement, so that the trials are independent. Compute the probability of each of the two sequences WWRWR and RWWWR.
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The solution contains a detailed explanation of the determination of probabilities in various situations.