The southeast regional manager of General Express, a private parcel-delivery firm, is worried about the likelihood of strikes by some of his employees. He has learned that the probability of a strike by his pilots is 0.75 and the probability of a strike by his drivers is 0.65. Further, he knows that if the drivers strike, there is a 90 percent chance that the pilots will strike in sympathy. (a) What is the probability of both groups' striking? (b) If the pilots strike, what is the probability that the drivers will strike in sympathy?

Consider two events following receiving a bachelor’s degree from a prestigious university: A = {being accepted into a graduate program} and B = {receiving a job offer}. We know the following is true: P(A) = P(B) = 0.7 P(A|B) = 0.9 Are events A and B independent? Why or why not?

You plan to go on a hike in spite of the fact that a tornado watch is in effect. The national weather service tells you that for every hour in your area, there is a 30 percent chance that a tornado will strike. That is, there is a 30 percent chance that a tornado will strike your area between 10 am and 11 am, a 30 percent chance that a tornado will strike your area between 11 am and noon, and so on. (a) What is the probability of a tornado striking your area at least once during a two-hour hike?(b) What is the probability of a tornado striking your area at least once during a four-hour hike?(c) What is the probability of a tornado striking your area at least once during a Eight-hour hike?

(6) A local university offers free flu shots to its employees. Of the eligible employees, 75% have the flu shot and 25% do not. Of the employees that take the flu shot, 10% actually get the flu. Of the employees that do not take the flu shot, 45% actually get the flu. What is the probability that a person who gets the flu took the flu shot? What is the probability that a person who does not get the flu did not have a flu shot?