4. First Bank of Springdale operates a one-lane drive-in ATM machine. Cars arrive according to a Poisson distribution at the rate of 12 cars per hour. The time per car needed to complete the ATM transaction is exponential with mean 6 minutes. The lane can accommodate a total of 10 cars. Once the lane is full, other arriving cars seek service in another branch. Determine the following:

(a) The probability that an arriving car will not be able to use the ATM machine because the lane is full.

(b) The probability that a car will not be able to use the ATM machine immediately on arrival.

(c) The average number of cars in the lane.