The number of Yankees fans shopping at a sports store in a given hour is Poisson with mean 8. The number of Red Sox fans shopping at the same store is Poisson with mean 6 per hour. Assume that the numbers of fans of the two types are independent. In particular, there is no person who is simultaneously a fan of both teams.
a. In a 3-hour period, how many Yankees and Red Sox fans do we expect altogether?
b. Find the probability that exactly one person enters the store during the next 20 minutes who likes the Yankees or Red Sox.