There are two traffic lights on Shelly’s route from home to work. Let E denote the event that Shelly must stop at the first light, and define the event F in a similar manner for the second light. Suppose that P (E) = 0.4, P(F) = 0.3, and P(E ∩ F) = 0.15.
a. Use the given probability information to set up a “hypothetical 1000” table with columns corresponding to E and not E and rows corresponding to F and not F.
b. Use the table from Part (a) to find the following probabilities:
i. The probability that Shelly must stop for at least one light (the probability of E ∪ F).
ii. The probability that Shelly does not have to stop at either light.
iii. The probability that Shelly must stop at exactly one of the two lights.
iv. The probability that Shelly must stop only at the first light.