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**Flower90** I need help to solve these exercises about Poisson processes:

1)Arrivals of the Number 1 bus form a Poisson process of rate one bus per hour, and arrivals of the Number 7 bus form an independent Poisson process of rate seven buses per hour.

a) What is the probability that exactly three buses pass by in one hour

b) What is the probability that exactly three Number 7 buses pass by while I am waiting for a Number 1?

c) When the maintenance depot goes on strike half the buses break down before they reach my stop. What, then, is the probability that I wait for 30 minutes without seeing a single bus?