Bob and Jane agree to meet at a known location between 2pm and 3pm. The problem
ID: 3075291 • Letter: B
Question
Bob and Jane agree to meet at a known location between 2pm and 3pm. The problem is that neither of them know what time the other will arrive.
We may assume that both of them are equally likely to arrive at any time between 2pm and 3pm.
However Bob is prepared to wait 10 minutes for Jane to arrive before leaving. And Jane is prepared to wait only 5 minutes for Bob to arrive before she leave.
a) If Bob arrived at 1.30 pm, what would be the probability that they meet?
If possible could you explain workings please , I had a hint that there a geomertic approach but I am not too sure on the apprach to that
Explanation / Answer
As Bob arrived at 1:30 pm. So, by the question, Jane could arrive at {1:25,1:26,.....1:29} or {1:31,1:32,.....1:40}. So, the no. of the favourable case is 15 whereas the number of total cases is 60. Since they agree to a known location between 2 pm and 3 pm.
Hence required prob. is 15/60=1/4=0.25