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 PA) and PY).

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.