Phone calls arrive at the Macrohard call center as a Poisson process with rate λ = 4 per minute. Eachcaller is independently either happy, annoyed or angry, with probabilities P(happy) = 0.1, P(annoyed) = 0.3, P(angry) = 0.6
a) Find the probability that the next caller is angry
b) Find the probability that two angry calls arrive in the next 30 seconds
c) Find the expected number of happy callers in the next hour.
d) Find the probability that at least two happy calls arrive before the next angry call
e) Given that 2 happy calls and 3 angry calls arrived between 3:00pm and 3:02pm, find the probability thatno calls arrived between 3:00pm and 3:01pm.