Probability Question

Question

A baker put 500 raisins into dough, mixed well, and made 100 cookies. You take a random cookie. What is the probability of finding at least 4 raisins in it? (Hint: use Poisson approximation to the Binomial distribution of the number of raisins in one cookie.)

Answer 1

Hello, thank you for taking the time to post your question!

It’s wanting you to compute the probability on this one using the Poisson approximation … what that means is that your starting point here would be finding the value of the parameter lambda, the average number of events in a given interval.

For this question that would be lambda = 500/100 = 5 raisins/cookie

What we’re trying to find then is the probability of there being at least 4 raisins in it, which would be P(X >= 4). Using a Poisson cumulative distribution function with those parameters, I find the underlying probability to be 0.7350.

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)