Question

A man and a woman agree to meet at a certain location about 12:30 p.m. if the man arrives at a time uniformly distributed between 12:15 and 12:45 and the woman independently arrives at a time uniformly distributed between 12:30 and 1 pm, find the probability that the man arrives first

Answer 1

we define the spaces of the man and the woman's independent arrivals.
In this case,
f(man) = 1 (45-15) = 1/30
f(woman)=1/(60-0)= 1/60
f(man)*f(woman) = 1/1800

Probability = P
P (man-woman)< 5 = 1/1800* integral of (y ) with limits of (x+5) and (x-5) from 45 to 15.
P (man-woman) <5 = 1/6