Answer to Question #213758 in Statistics and Probability for ish

Question

 An average of 10 cars per hour arrive to the bank at a single server drive-in teller. Assume that the average service time for each customer is 4 minutes, and both interarrival and service times are exponential. What is the probability that the arriving car waits for the teller. 

Answer 1

If the arriving car waits for the teller, It means that the teller is working rather than being idle.

$M/M/1$ with $\lambda=10cars/hour$ and $\mu =15cars/hour$

Therefore, the probability that the arriving car waits the teller is

$P\left(car\:waits\:for\:teller\right)=\frac{\lambda }{\mu }=\frac{10}{15}$

$P\left(car\:waits\:for\:teller\right)=\frac{2}{3}$