Suppose that at a famous aquarium, a docent found that 35 percent of elementary school children know the difference between dolphins and porpoises. If a docent has a tour group that has 9 elementary school children, what is the probability that at least two of the children know the difference between dolphins and porpoises? In a fantasy world, there is a region called Durotar, where about 68 percent of the denizens are orcs. If we happen upon a group of 7 denizens, what is the probability that the number of orcs is at least 2 and less than 5.8

5. A manufacturer of cell phones purchases batteries from a vendor. It is not uncommon to receive defective batteries from this vendor, thus whenever a shipment is received, a sample of batteries is inspected. For this month's shipment, a random sample of 280 batteries is selected and each battery is inspected. If the proportion of defective batteries sampled is more than 1.5%, the entire shipment will be returned to the vendor. What is the probability that this month's shipment will be returned if the true proportion of defective batteries is 4%?

20. Based on student records, 25% of the students at a large high school have a GPA of 3.5 or better, 16% of the students are currently enrolled in at least one AP class, and 12% of the students have a GPA of 3.5 or better and are enrolled in at least one AP class. If we select one student at random, what is the probability that the student has a GPA lower than 3.5 and is not taking any AP classes? (A) 0.29 (B) 0.47 (C) 0.53 (D) 0.63 (E) 0.71

section 5.5   A personnel director has two lists of applicants for jobs. List 1 contains names of 24 women and 8 men, whereas List 2 contains the names of 9 women and 16 men. A name is randomly selected from List 1 and added to List 2. A name is then randomly selected from the augmented List 2. Given that the name selected is that of a man, what is the probability that a woman's name was originally selected from List 1? Round your answer to four decimal places, if necessary.