Grinstead-Snell-Probability · Problem 5.1.22

Distributions and Densities

Mathematics · poisson-distribution

Problem

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,…0, 1, 2, \ldots raisins. Consider the cookies as trials in an experiment, and let XX 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 n=600n = 600 independent trials with probability p=1/500p = 1/500 for success on each trial. Since nn is large and pp is small, we can use the Poisson approximation with λ=600(1/500)=1.2\lambda = 600(1/500) = 1.2. Determine the probability that a given cookie will have at least five raisins.

Related theory

Browse the problem library