Two mathematicians take a morning coffee break each day. They arrive at the cafeteria independently, at random times between 9 AM and 10 Am, and stay exactly for M minutes. Find the value of M if the probability that either one arrives while the other is in the cafeteria is 40%.
i don't get it :(

Question

Two mathematicians take a morning coffee break each day. They arrive at the cafeteria independently, at random times between 9 AM and 10 Am, and stay exactly for M minutes. Find the value of M if the probability that either one arrives while the other is in the cafeteria is 40%.
i don't get it :(

dumbcow · Answer

the probability that they are in cafeteria at same time is 40%, this means 2nd person arrives while 1st is sill eating
Let the times they arrive be X,Y respectively
so 1st person stays between X and X+M
probability that Y is in that interval is 0.4
since arrival time is random and uniform, you can say that probability of Y in [X,X+M] = M/60
--> M/60 = 0.4 --> M = 24

dumbcow · Answer

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