Please show your work

7. (10 points) Baseball Fans The number of Yankees fans shopping at a sports store, per hour, is Poisson with mean 8 per hour. 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) (5 points) In a three hour period, how many Yankees and Red Sox fans do we expect altogether? (b) (5 points) Find the probability that exactly 1 person enters the store during the next 20 minutes who likes the Yankees or Red Sox