I am preparing for my Probability's exam, after going through Continuous Distributions, I decided to attempt some exercise questions, and heres a question that has left me completely clueless.
It states that,
The arrival time of People entering in an ice parlor are poisson distributed with rate of 50/hour. Any particular person buy an ice cream with probability of 1/4.
What is the distribution of time until the first scoop of ice cream is sold?
What is the probability that no ice cream is sold in a particular hour?
As both the questions are related to Time that means, I believe, Exponential distribution should be used, with parameter 50, but I am not sure how to incorporate the probability of buying an ice cream in my solution!
Kindly guide me, thank you!