Does anyone know how to solve this question?
Traffic on a road follows a Poisson process with rate $\displaystyle \frac 23$'s of a car per minute. $10$% of vehicles are trucks and the other $90$% are cars.
a) What is the probability at least one truck passes in an hour?
b) Given that $10$ trucks have passed by in an hour, what is the expected number of total vehicles that have passed by?
c)Given that $50$ vehicles have passed by in an hour, what is the probability there were exactly $5$ trucks and $45$ cars?
Cheers