Poisson Distribution

p(0) = 0.0183, or 1 chance in 55.

Explanation

We need only consult the Poisson Table for r = 4 (the average number of raisins per final cookie) to get the full range of variation to be expected of the cookies in the batch. We are presently interested in the figure p(0), which turns out to be 0.0183, or roughly 1 in 55. Still more roughly, the odds are that such a result will turn up twice in a batch of 100 cookies: 100 times 0.0183 = 1.83 ~ 2.

Comment

A word of caution. In order to qualify as a Poisson problem, the batter in question needs to be defined as the output of a batter making machine with a 4-per-cookie tendency, and not as the result of one batch with a precisely known number of raisins in it: compare the contrast presented in Problem 5c. Many textbook problems meant for the Poisson chapter of some book retain, in this way, habits of thinking formed in the Binomial chapter of that book. Be alert when using other textbooks, and for that matter, be alert in general.