I am not sure about my answer. In particular, part b of the following question.
Pizza orders arrive according to a Poisson process of rate 20 per hour. Orders are independently for a vegetarian pizza with probability 1/ 4 , and for a meat pizza with probability 3/4
a. Six orders arrived between 6:45pm and 7:00pm. Given this, what is the probability that fourteen orders arrive between 7:00pm and 7:45pm?
My Attempt: Let $t=$ time in min. So $\lambda$ per mininute=$20/60=1/3$
b. During a particular 60 minute period, 4 vegetarian orders were received. What is the probability that all 4 of them came during the first 30 minutes?
The conditional poisson would be uniform distributed between (0,60).