Poisson Distribution
Answer 7a

5 raisins per cookie (r = 5), or 500 per batch of dough

Explanation

This way of stating the cookie problem is due to Feller. We have the requirement that p(0) = 0.0100. The easy way to get the answer is to scan along the top or p(0) line of the Poisson Table, to find the smallest value of r for which the value of p(0) is 0.0100 or less. This turns out to be r = 5, for which p(0) = 0.0067. At this level of raisins, a raisinless cookie will turn up only every 150 cookies. The first batch of 100 cookies seems moderately well protected.

Comment

On the other hand, suppose you bake a second batch? Suppose you are running a home business making refrigerator cookies? Suppose your middleman, the guy in the frozen food truck, holds out to you a partly sliced roll of frozen cookie dough and says, "Mrs Beauregard found that her third cookie from this roll had no raisins at all in it." What then?

24 Aug 2007 / Contact The Project / Exit to Resources Page