Problem
There are two traffic lights on the route used by a certain individual to go from home to work. Let E de- note the event that the individual must stop at the first light, and define the event F in a similar manner for the second light. Suppose that P 1E 2 = .4, P 1F 2 = .3, and P 1E n F 2 5 .15.
a. What is the probability that the individual must stop at at least one light; that is, what is the probability of the event E U F ?
b. What is the probability that the individual needn't stop at either light?
c. What is the probability that the individual must stop at exactly one of the two lights?
d. What is the probability that the individual must stop just at the first light? (Hint: How is the probability of this event related to P 1E 2 and P 1E n F 2 ? A Venn diagram might help.)
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.