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In: Statistics and Probability

Alice and Bob bet 50 dollars with each other in a game in which their friend...

Alice and Bob bet 50 dollars with each other in a game in which their friend Charlie tosses a two-sided coin 3 times in a remote location. If Alice correctly predicts the majority face (i.e. the face which occurred the most often in the three tosses), she gets to keep Bob's money as well. Charlie calls them and lets them know that at least 1 heads has occurred.a) Assuming that the coin was fair, what is the probability that the majority face was indeed heads? Based on your answer, whichface do you think Alice should declare as the majority face? b) Now suppose that the coin was biased with one third probability of heads. Find the probability of the above event again, i.e., the event that heads is a majority face. Based on your answer, which face do you think Alice should declare as the majority face?

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Expert Solution

Fair coin

for biased coin see below

orchestra answered 2 years ago
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