On a recent holiday evening, a sample of 500 drivers was stopped by the police. Three hundred were under 30 years of age. A total of 250 were under the influence of alcohol. Of the drivers under 30 years of age, 200 were under the influence of alcohol.Let A be the event that a driver is under the influence of alcohol.Let Y be the event that a driver is less than 30 years old.
a.Determine P(A) and P(Y).b.What is the probability that a driver is under 30 and not under the influence of alcohol?c.Given that a driver is not under 30, what is the probability that he/she is under the influence of alcohol?d.What is the probability that a driver is under the influence of alcohol, when we know the driver is under 30?e.Show the joint probability table.f.Are A and Y mutually exclusive events? Explain.g.Are A and Y independent events? Explain.?
What will be an ideal response?
?
| a. | P(Y) = 0.6 P(A) = 0.5 | |||
| b. | 0.2 | |||
| c. | 0.25 | |||
| d. | 0.667 | |||
| e. | A | A c | ||
| Y | 0.4 | 0.2 | ||
| Yc | 0.1 | 0.3 | ||
| f. | No, P(A?Y) ? 0 | |||
| g. | No, P(A ? Y) ?P(A) | |||
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