You and a friend, along with an eccentric rich probabilist, areobserving a Poisson process whose arrival rate is λ = .5 per hour.The probabilist offers to pay you $100 if there is at least onearrival between noon and 2pm, and also offers to pay your friend$100 if there is at least one arrival between 1pm and 3pm.
a. What is the probability that either you or your friend, orboth, gets $100?
b. What is the probability that one of you wins $100, but notboth?
Consider a Poisson process with arrival rate λ per minute. Giventhat there were three arrivals in the first 2 minutes, find theprobability that there were k arrivals in the first minute; do thisfor k = 0, 1, 2, and 3.
Given that P(A) = .4, P(A ∩ B) = .1, and P((A ∪ B) c ) = .2,find P(B).
