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•• A coin is flipped N times. The probability that the coin will come up heads all N times is P(N) = 1/2N. (a) Show that this probability can also be written as P(N) = 10−N ln 2/ln 10. [Hint: Note that x = eln x = 10log x, from which it follows that ln x = ln[10Iog x] = (log x)(ln 10).] (b) For what value of N does the probability of N heads in a row fall below 10−8? (10−8 is about the probability of winning a large state lottery.)
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