` 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.
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