2. DRUNK DRIVERS IN OHIO A study was recently undertaken to analyze the relation

Question

2. DRUNK DRIVERS IN OHIO A study was recently undertaken to analyze the relationship between the number of drunk drivers in Ohio between the ages of 16 and 45 and whether each were first time offenders or repeat offenders. The data obtained from this study is given below: Age First Time Offender Repeat Offender 16-20 5,311 519 10.713 4.104 10,301 5,719 8.246 4,344 2,596 36-40 5.442 3.474 1,719 Suppose that a drunk driver from this study is chosen at random. 1. What is the probability that the drunk driver is a repeat offender? 2. What is the probability that the drunk driver is under 21 years of age or a first-time offender? 3. If the drunk driver turns out to be over 30, what is the probability that he/she is a repeat offender: 4. Is a first time offender or a repeat offender more likely to be over 30?

Explanation / Answer

1. Probability that the drunk driver is a repeat offender = (519 + 4104 + 5719 + 4344 + 2596 + 1719) / (519 + 4104 + 5719 + 4344 + 2596 + 1719 + 5311 + 10713 + 10301 + 8246 + 5442 + 3474) = 0.3041.

2. Probability that the drunk driver is under 21 years of age or a first time offender = (5311 + 10713 + 10301 + 8246 + 5442 + 3474 + 519) /  (519 + 4104 + 5719 + 4344 + 2596 + 1719 + 5311 + 10713 + 10301 + 8246 + 5442 + 3474) = 0.7042.

3. Probability that the driver is a repeat offender given that the driver is over 30 = (4344 + 2596 + 1719) / (4344 + 2596 + 1719 + 8246 + 5442 + 3474) = 0.3353.

4. Probability that a first time offender is over 30 = (8246 + 5442 + 3474) / (5311 + 10713 + 10301 + 8246 + 5442 + 3474) = 0.3946.

Probability that a repeat offender is over 30 = (4344 + 2596 + 1719) / (519 + 4104 + 5719 + 4344 + 2596 + 1719) = 0.4557.

Clearly a repeat offender is more likely to be over 30.

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