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Men and women arrive at a store according to independent Poisson processes with hourly rates $\lambda_M$ = 3 and $\lambda_F$ = 4, respectively. Men shop for a time that is uniformly distributed on [0, 1], and women shop for a time that is uniformly distributed on [0, 2] (in hours).

Given that a man arrived during the interval [4, 5], what is the probability that he is still in the store at time 5?

Since it's a poisson process, the interval is independent of the other intervals. Let x be the time the man arrives ie. $x\in[4,5]$. Does that mean the probability is 5-x? Apparently it's supposed to be half.

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