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

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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

21-25

10,713

4,104

26-30

10,301

5,719

31-35

8,246

4,344

36-40

5,442

2,596

41-45

3,474

1,719

Suppose that a drunk driver from this study is chosen at random.

What is the probability that the drunk driver is a repeat offender?

What is the probability that the drunk driver is under 21 years of age or a first-time offender?

If the drunk driver turns out to be over 30, what is the probability that he/she is a repeat offender?

Is a first time offender or a repeat offender more likely to be over 30?

Age

First Time Offender

Repeat Offender

16-20

5,311

519

21-25

10,713

4,104

26-30

10,301

5,719

31-35

8,246

4,344

36-40

5,442

2,596

41-45

3,474

1,719

Explanation / Answer

What is the probability that the drunk driver is a repeat offender?
There are 62488 total offenders including both first time and repeat.
there are total 19001 repeat offenders.
Hence the probability that the drunk driver is a repeat offender = 19001/62488 = 0.3041

What is the probability that the drunk driver is under 21 years of age or a first-time offender?
Number of drunk driver under 21 years of age = 5830
Number of first time offenders = 43487
Number of drunk driver is under 21 years of age and a first-time offender = 5,311

Required probaibility = (5830 + 43487 - 5,311)/62488 = 0.7042

If the drunk driver turns out to be over 30, what is the probability that he/she is a repeat offender?
P(over 30) = 25821/62488 = 0.4132
P(repeat offender and over 30) = 8659/62488 = 0.1386

P(repeat offender | over 30) = 0.1386/0.4132 = 0.3354

Is a first time offender or a repeat offender more likely to be over 30?
P(first time offender and over 30) = 8659/62488 = 0.1386
P(repeat offender and over 30) = 17162/62488 = 0.2746

No, a first time offender or a repeat offender more likely to be over 30.