There are two traffic lights on Darlene's route from home to work. Let E denote the event that Darlene must stop at the first light, and define the event F in a similar manner for the second light. Suppose that

P(E) = 0.3, P(F) = 0.3, and P(E F) = 0.13.

Solve all

(a)

What is the probability that Darlene must stop at at least one light; that is, what is the probability of the event

P(E F)?

b. What is the probability that Darlene doesn't have to stop at either light?

c What is the probability that Darlene must stop at exactly one of the two lights?

d What is the probability that Darlene must stop just at the first light? (Hint: How is the probability of this event related to

P(E) and P(E F)? A Venn diagram might help.)