Suppose that the time between entrance of two consecutive customers to a store follows an exponential distribution of mean 2 minutes. A person is observing this store at a time and see there are no customers inside. what is the probability that after 5 minutes, no customers enter the shop.
I think the answer is very easy. Because exponential distribution is memoryless We simply find $P(X\geq 5) = 1-P(X\leq5) = 1-( 1 - e^{- \frac{1}{2} 5}) = e^{-\frac{1}{2} 5}$
Is my reasoning correct? it seems the problem is very easy but I found this in an exam and it was marked as medium difficulty.