A man and a woman agree to meet at a certain location about 12:30 pm. If the man arrives at a time uniformly distributed between 12:15 pm and 12:45 pm, and if the woman independently arrives at a time uniformly distributed between 12:00 pm and 1 pm, find the probability that the first to arrive waits no longer than 5 minutes. What is th

A man and a woman agree to meet at a certain location about 12:30 pm. If the man arrives at a time uniformly distributed between 12:15 pm and 12:45 pm, and if the woman independently arrives at a time uniformly distributed between 12:00 pm and 1 pm, find the probability that the first to arrive waits no longer than 5 minutes. What is the probability that the man arrives first?

1/2

Step-by-step explanation:

What is the probability that the man arrives first?

Define random variables X And Y that marks the time at which the man and women arrives at a certain place.

Representing their precise times of arrival are 12: X and 12: Y.

It is given that X ~ Unif(15, 45) and Y Unif(0, 00) and that these variables are independent.

We are required to find the probability that the distance between these two arrivals will be longer than 5 minutes, ie.

Check the figure below

The probability that the man arrives first is P(X <Y).

But, observe the variables X and Y are symmetric around the same point 12: 30.

Hence we can say that none of them is at an advantage to arrive first.

Thus P(X <Y) = 1/2

problem:

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

f(5/2) = 10/3

i hope this !