Problem 39E

If a parachutist lands at a random point on a line between markers A and B, find the probability that she is closer to A than to B. Find the probability that her distance to A is more than three times her distance to B.

Solution :

Step 1 of 1:

Given if a parachutist lands at a random point on a line between marker A and B.

Our goal is:

We need to find the probability that she is closer to A and we need to find the probability that her distance to A more than times her distances to B.

Now we have to find the probability that she is closer to A and now we have to find the probability that her distance to A more than times her distances to B.

Here the distance Y is uniformly distributed on the interval A to B.

If she is closer to A, she has landed in the interval .

This is one half of the total interval length, so the probability is 0.5.

If her distance to A is more than three time her distance to B, she has landed in the interval .

This is one quarter the total interval length.

So the probability is 0.25.