Three people are to be seen in a certain place at 10 o\'clock in the morning. Ea

Question

Three people are to be seen in a certain place at 10 o'clock in the morning. Each person arrives at the place of the appointment independently in a random time evenly distributed between 10 and 11 in the morning. Each person waits 10 minutes and, if there is no other, he leaves; On the other hand, if they can find 2 of them, they wait for the other until 11 in the morning. A) What is the probability that no pair of people will be found? B) What is the probability that the 3 persons will be found? C) What is the least time that each person should wait in such a way that the probability that the 3 are found is greater than 1/2?

Explanation / Answer

a) no pair will be found means the difference in arrival time of the three person is more than 10 minutes i.e 11 minute or more

first person can arrive from 10 to 10:38 ,second person can arrive from 10:11 to 10:49 ,third person can arrive from 10:22 to 10:60(11).

first person probaility is 38/60=0.633,second person =39/60=0.633 similarly third person probability=0.633

total probability=(0.633)3=0.2536

b) three peron will be found means two persons coming in 10 minutes period and third one come after two person

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