Finding Geometric Probability

(of area, that is)

What is geometric Probability?

Geometric Probability, or at least this kind, is the probabilty that a point lies in a specific region of a shape. Some questions may look like so:

What is the percentage that a point may lie within the blue triangle (shaded region) within the red circle. (This question's picture is at right)

How to find the Probability

First, find area of entire region containing any others. Then find the specific area of the shape inside it you are instructed to find, whether you have to subtract it out or that it is given.

Next, you need to find the percentage of area the smaller shape covers of the larger one. Set up a proportion so that the smaller shapes area is to the entire region's area, as x is to 100. Solve.

Congrats! That's all there is to it!

An Example

Question- find probability that a point lies in the outer circle

First step- find area of the entire region. (circle area is pi times r^2.) 5 squared is 25, and you can leave it as 25 times pi for now. Next, find the area of the center circle. 3 squared is 9. Leave it as 9 times pi. Subtract 9 pi from 25 pi to find the outer circle's area.

Next step- Set it up as a proportion. 16 pi is to 25 pi as x is to 100. Solve.

You should end up with......... about 64%! The probability that a point lies in the outer circle is 64 percent. That should be where you place your bets!