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Question

The Federal Bureau of Investigation reported that in 2007, there were 7,624 incidents of hate crimes that had a bias motivation based on race, religion, sexual orientation, nationality, or disability. Of these incidents, 6,965 were committed by a “known offender,” where one or more attributes is known about the offender. If one incident is selected at random, find the probability that the incident was committed by a known offender.

Solution

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Define $P(E)$ to be the probability of an event $E$ where

$P(E)=\frac{\text{Number of favorable outcomes in E}}{\text{Total number of outcomes}}=\frac{n(E)}{n(S)}$

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