Probability of a-b > 3 in Randomly Selected Intervals

[ee1215]

Homework Statement

On the real line (-inf, inf), point a resides in the interval 0<=a<=4, and point b is in the interval -3<=b<=0; otherwise, points a and b are selected at random within their intervals. Find the probability that a-b is greater than 3.

Homework Equations

The Attempt at a Solution

So, 0<=a<=4 and -3<=b<=0 then 0<=a-b<=7. So is the probability that a-b is greater than 3, 4/8? There are 8 chances and only 4 probabilities that it could happen, 4,5,6,7.

 

[Dick]

Your choices aren't limited to integers. Draw the region of possible values of a and b in a two dimensional plane where one axis is a and the other is b. It's a rectangle, right? What fraction of that rectangle will satisfy a-b>=3? Find the line that bounds that region.