Question

Two friends A and B decided to meet in a restaurant between 6:00 PM and 7:00 PM on a Monday. They decided to wait for only 20 minutes. In these 20 minutes, if the other person does not come, the
will not meet What is the probability that they will not meet between 6:00 PM and 7:00 PM?​

Answer 1

Answer:

Two friends A and B decided to meet in a restaurant between 6:00 PM and 7:00 PM on a Monday. They decided to wait for only 20 minutes. In these 20 minutes, if the other person does not come, the

will not meet What is the probability that they will not meet between 6:00 PM and 7:00 PM?

Step-by-step explanation:

Let me see if I can make some other solution, by considering the discrete case.

Assume the arrivals happen only on the minutes, 0, 1, 2, 3 . . . 59, 60 (between 1PM and 2PM)

Number of cases of arrivals 61*61 = 3721.

If A arrives at 0, B can arrive at 0-15 (16 cases)

If A arrives at 1, B can arrive at 0-16 (17 cases)

If A arrives at 2, B can arrive at 0-17 (18 cases)

If A arrives at 3, B can arrive at 0-18 (19 cases)

.

.

.

If A arrive at 15, B can arrive at 0-30 (31 cases)

If A arrive at 16, B can arrive at 1-31 (31 cases)

If A arrive at 17, B can arrive at 2-32 (31 cases)

.

.

.

If A arrives at 44, B can arrive at 29-59 (31 cases)

If A arrives at 45, B can arrive at 30-60 (31 cases)

If A arrives at 46, B can arrive at 31-60 (30 cases)

.

.

.

If A arrives at 56, B can arrive at 41-60 (20 cases)

If A arrives at 57, B can arrive at 42-60 (19 cases)

If A arrives at 58, B can arrive at 43-60 (18 cases)

If A arrives at 59, B can arrive at 44-60 (17 cases)

If A arrives at 60, B can arrive at 45-60 (16 cases)

Hence total success cases will be 16+17+18+19....30 (15 numbers) + 31+31 (31 numbers) + 30+29+....17+16(15 numbers) which is 345+961+345=1651

Probability=1651/3721=0.444

Answer by or = 7/16= 0.438.

When we can consider smaller discrete intervals of time (eg arrivals can occur on the second, 00:00,00:00:01,... 00:00:57,00:00:58,00:00:59,00:01:00,... 00:59:57,00:59:58,00:59:59,01:00:00), we get more closer to the exact answer.

When taking the limit (as time between possible arrivals tending to 0), we will get the same answer 7/16.