1. The number of chocolate chips in a chocolate chip cookie is Poisson with a mean of 3. a) What is the probability (mass) function for the number of cookies that would have to be drawn until one gets a cookie with at most one chocolate chip in it? b) A bag of cookies has 2 cookies with at most one chocolate chip and 8 cookies with more than one chocolate chip. If Sarah and Sam split the bag evenly (5 cookies each) at random, what is the probability that Sarah gets both cookies with at most one chocolate chip? 2. Show that the binomial probability function is unimodal in x (i.e., p(x) either always increases in x; or only decreases in x; or increases to a maximum and then decreases as x goes from 0 to n). Hint: Consider p(x)/p(x-1).