Fifty Challenging Problems in Probability with Solutions by Frederick Mosteller

Author:Frederick Mosteller
Language: eng
Format: epub, pdf
ISBN: 9780486134963
Publisher: Dover Publications
Published: 2012-10-11T00:00:00+00:00

(A)

We want to eliminate the terms corresponding to odd numbers of cakes. Recall that

(B)

The sum of expressions (A) and (B) would give us twice the probability of an even number of loaves because the terms with odd powers of m would add to zero and the terms with even powers would have a coefficient of 2. Consequently, after dividing by 2, we get for the probability of an even number (1 + e—2m)/2. For m = 20 the result is extremely close to 0.5 because e—40 is negligible.

On the other hand, if he sold on the average one special birthday cake per trip over the route, the probability that he sells an even number of special birthday cakes is about 0.568.

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