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Crime rates per 100,000 give rape totals of 29.7, 29.1, 27.7 and 26.8 for the years 2008 to 2011. What is the probability of 2011 given rape?
AIt is about 0.0059
BIt is about 0.2365
CIt is about 0.2575
DIt is about 0.1551
Answer & Solution
Correct answer: B. It is about 0.2365
1. Conditioning on rape reduces the sample space to the rape column alone.
2. That column totals 29.7 plus 29.1 plus 27.7 plus 26.8, which is 113.3.
3. The 2011 entry in that column is 26.8.
4. Dividing 26.8 by 113.3 gives 0.2365.
5. Dividing 26.8 by the grand total of 4,520.7 instead gives about 0.0059, which is the joint probability.
6. The value 0.2575 belongs to a different conditional, vehicle crime given the year 2008.
_Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 3 "Probability Topics", section 3.4 Contingency Tables and Probability Trees_
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