# Math Help - Geometric Probability

1. ## Geometric Probability

What is the probability for a point chosen at random is in the smallest circle? These are in inches. Sorry for the crappy diagram..

2. Originally Posted by lynn0218
What is the probability for a point chosen at random is in the smallest circle? These are in inches. Sorry for the crappy diagram..

If you assume that any point can be chosen from the diagram you drew with equal probability, the probability that it will land in the smaller circle is just the area of the smaller circle divided by the total area, i.e.

$X = \text{event that randomly chosen point lands in the inner circle}$

$P(X) = \frac{\pi r_s^2}{\pi r_t^2} = \frac{4\pi}{36\pi} = \frac{1}{9}$

here $r_s = 2$ is the small circle radius and $r_t = 6$ is the total circle radius.