4.

a. Harold and Maude plan to take a cruise together, but they live in separate cities. The cruise departs from Miami, and they each book a flight to arrive in Miami an hour before they need to be on the ship. Their travel planner explains that Harold's flight has an 80% chance of making it on time for him to get to the ship, and Maude's flight has a 90% chance of making it on time.

a. How do you think the travel planner determined these probabilities.

b. Whether realistic or not, assuming the probabilities are independent, what is the probability that Harold and Maude will both arrive on time?

b. Suppose that a magnet high school includes grades 11 and 12, with half of the students in each grade. Half of the senior class and 30% of the junior class is taking calculus. A calculus student is randomly selected to accompany the math teachers to a conference. What is the probability that the student is a junior?

c. A professor has noticed that, even though attendance is not a component of the grade for his class, students who attend regularly obtain better grades. In fact, 40% of those who attend regularly receive A's in the class, while only 10% of those who do not attend regularly receive A's. About 70% of students attend class regularly.

a. Find the probability that a randomly selected student will receive an A given that the student attends class regularly.

b. Find the probability that a randomly selected student will receive an A given that the student does not attend class regularly.

c. Find the overall probability that a randomly selected student will receive an A.

d. Recall from Chapter 2 that the median of a data set is the value with half of the observations at or above it and half of the observations at or below it. Suppose four individuals are randomly selected with replacement from a large class and asked how many hours they studied last week. Assume that there are an even number of students in the class and that nobody has a response exactly equal to the median. What is the probability that all four individuals will give a response that is above the median for the class?