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A large number of people claim that an alien spacecraft crash-landed in Roswell, New Mexico. Let E be the event that this claim is true and let R be the event that large numbers of people report it to be true.

a. If Pr(R|E) = 1 and Pr(R|~E) = q < 1 find the posterior belief that E is true given R for someone who has a prior belief p

b. Show that the posterior belief is decreasing in q and increasing in p. Explain

c. Show that someone will think that the claim has more than a fifty percent chance of being true if p > q / (1 + q). Explain.

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