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.
The entries in the model are mutually exclusive. That means, if there are 1 waiters and 2 chefs, there are not 2 waiter and 2 chefs for example!
So, that means all the probabilities together must sum to 1. So we have:
1 - 0.03 - 0.02 - 0.02 - 0.04 - 0.01 - 0.01 - 0.04 - 0.05 - 0.04 - 0.05 - 0.66 = k
k = 1-0.97
k = 0.03
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