A restaurant needs a staff of 3 waiters and 2 chefs to be pr

A restaurant needs a staff of 3 waiters and 2 chefs to be properly staffed. The joint probability model for the number of waiters (X) and chefs (Y) that show up on any given day is given below.

a) What must the value of k be for this to be a valid probability model?  

b) What is the probability that at least one waiter and at least one chef show up on any given day?  

c) What is the probability that more chefs show up than waiters on any given day?  

d) What is the probability that more than three total staff (waiters and chefs) will show up on any given day?

Solution