Please write in clear handwriting. Thank you very much.

[1|] marks] Bob has arrived at the side of the road and started to hitchhike. He is currently there alone, but other hitchhikers arrive according to a Poisson process with rate A = 1 per hour. Cars pass by according to an independent Poisson process with hourly rate p. 3:- 1. Any arriving car picks up a single hitchhiker, and Bob, being a nice guy, takes a ride only if nobody else waits. All hitchhikers wait until picked a) [4 marks] What is the probability that Bob waits there alone (Len, neither a car nor another hitchhiker arrives) during at least 30 minutes? b} [3 marks] 'What is the probability that Bob gets picked up by the rst car (Le.T before another hitchhiker arrives)? c} [3 marks] What is the probability that Bob gets picked up by the second car