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Suppose an automobile insurance company classifies a driver as good, average, or bad. Of all their insured drivers, 25% are classified good, 50% are average, and 25% are bad. Suppose for the coming year, a good driver has a 5% chance of having an accident, and average driver has 15% chance of having an accident, and a bad driver has a 25% chance. If you had an accident in the past year what is the probability that you are a good driver?

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rodolforodriguezr

Answer:

8.33%

Step-by-step explanation:

By Bayes' Theorem

[tex]P(Good|Had Accident)=\\=\frac{P(Had Accident|Good)P(Good)}{P(Had Accident|Good)P(Good)+P(Had Accident|Average)P(Average)+P(Had Accident|Bad)P(Bad)}=\\=\frac{0.05*0.25}{0.05*0.25+0.15*0.50+0.25*0.25}=0.0833=8.33\%[/tex]

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