Eddie L'Amore gets an average of 3 customers a day.
On any given day what is the probability that he has a prime number of customers?
Assumptions :
The occurrence of customers is uncorrelated, and the customer probability distribution doesn't vary from day to day, so you can assume the number of daily customers follows a Poisson distribution .
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You can assume a Poisson distribution. So
P ( n ) = n ! k n e − k . where k = 3 .
So P (prime) = P ( 2 ) + P ( 3 ) + P ( 5 ) + P ( 7 ) + . . . . = 0 . 5 7