The number of female customers arriving to a coffee shop followa Poisson process with a mean rate of 3 per hour. The number ofmale customers arriving to the same coffee shop also follow aPoisson process with a mean rate of 6 per hour and their arrival isindependent of the arrivals of female customers.
a) What is the probability that the next customer will arrivewithin 5 minutes?
b) What is the probability that exactly thee customers willarrive in the next 5 minutes?
c) What is the probability of exactly two male and exactly onefemale customer will arrive in the next 5 minutes?
d). Parts b) and c) ask for the probability of exactly threearrivals in the next 5 minutes. Are they identical? Explainwhy?
e) What is the probability of exactly five customers will arrivebetween 6 and 7 hours from now?
