A company is studying accident rates among its drivers. 70% of its drivers are classified as standard while 30% are classified as high risk. High risk drivers are 10 times more likely to have an accident as a standard driver. A randomly selected driver had an accident. Find the probability the driver is high risk.
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Given that high risk drivers are 10 times more likely to have an accident as a standard driver, we have: \[ P(\text{accident | standard}) = \frac{1}{10} \times P(\text{accident | high risk}) \] Show more…
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An insurance company classifies drivers as low-risk, medium-risk, and high-risk. Of those insured, 60% are low-risk, 30% are medium-risk, and 10% are high-risk. After a study, the company finds that during a one-year period, 1% of the low-risk drivers have an accident, 5% of the medium-risk drivers have an accident, and 9% of the high-risk drivers have an accident. If a driver is selected at random, find the probability that the driver will have an accident during the year.
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