Aman and a woman agree to meet at a cafe about noon. if the man arrives at a time uniformly distributed between 11: 40 and 12: 10 and if the woman independently arrives at a time uniformly distributed between 11: 45 and 12: 20, what is the probability that the first to arrive waits no longer than 5 minutes?

0.3888

Step-by-step explanation:

To solve the exercise we need a neutral time, so we define at 12:00 as time 0.

If the man arrives in a uniformly distributed time between 11:40 and 12:10, the time is distributed from -20 to 10.

If the woman arrives in a time evenly distributed between 11:45 and 12:20, the time is distributed from -15 to 20.

Assuming that each one arrives at 12: X and 12: Y for men and women, then the space of our time is defined as

Man [-20,10]

Woman [-15,20]

So,

Then,

The probability of finding an arrival less than 5 minutes is

answer is 67%

step-by-step explanation: