Astronomers estimate that as many as 100 billion stars in the Milky Way galaxy may be encircled by planets. Let p denote the probability that any such solar system contains intelligent life.
How small can p be and still give a 50-50 chance that there is intelligent life in at least one other solar system in our galaxy? (Hint: Use the probability distribution designed to handle problems where the probability is small and n is large.)
A statistically-minded fraternity man keeps records on how many women he must ask before one of them says she will be his date for a Saturday football game. His school plays five home games and his five acceptances come on the third, sixth, fourth, second, and ninth women he asks. Assume that the probability, p, that any woman he asks will accept his invitation is constant from woman to woman. Estimate p.