Question

Måns waits for the bus.The waiting time,T,until a bus comes is U(0,a) distributed. While he waits he tries to get a ride from cars that pass by according to a Poisson process with intensity λ. The probability of a passing car picking him up is p. Determine the probability that M ̊ans is picked up by some car before the bus arrives.

Remark. All necessary independence assumptions are permitted.

The answer is 1-(1- e^(−λpa) )/λpa

Answer 1