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

http://i50.tinypic.com/rs7dkg.jpg

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- Feb 12th 2010, 08:24 PMlynn0218Geometric 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..

http://i50.tinypic.com/rs7dkg.jpg - Feb 12th 2010, 09:10 PMlgstarn
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.

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

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

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