[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

Assume that we are making raisin cookies. We put a box of

600 raisins into our dough mix, mix up the dough, then make from the dough 500 cookies. We then ask for the probability that a randomly chosen cookie will have 0, 1, 2, \dots\ raisins. Consider the cookies as trials in an experiment, and let [math]X[/math] be the random variable which gives the number of raisins in a given cookie. Then we can regard the number of raisins in a cookie as the result of [math]n = 600[/math] independent trials with probability [math]p = 1/500[/math] for success on each trial. Since [math]n[/math] is large and [math]p[/math] is small, we can use the Poisson approximation with [math]\lambda = 600(1/500) = 1.2[/math]. Determine the probability that a given cookie will have at least five raisins.