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.
Question 2
In the two upcoming basketball games, the probability that UTC will defeat Marshall is 0.63, and the probability that UTC will defeat Furman is 0.55 . The probability that UTC will defeat both opponents is 0.3465.
a. What is the probability that UTC will defeat Furman given that they defeat Marshall?
b. What is the probability that UTC will win at least one of the games?
c. What is the probability of UTC winning both games?
d. Are the outcomes of the games independent? Explain and substantiate your answer.
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