A study has shown that the probability distribution of X, the number of customers in line (including the one being served, if any) at a checkout counter in a department store, is given by P(X = 0) = 0.25, P(X = 1) = 0.25, P(X = 2) = 0.20, P(X = 3) = 0.20, and P( ≥4 ) = 0.10. Consider a newly arriving customer to the checkout line.
a. What is the probability that this customer will not have to wait behind anyone?
b. What is the probability that this customer will have to wait behind at least one customer?
c. On average, behind how many other customers will the newly arriving customer have to wait?