91Ó°ÊÓ

White Cats and Deafness. Although cats generally possess an acute sense of hearing, due to an anomaly in their genetic makeup, deafness among white cats with blue eyes is quite common. Approximately \(95 \%\) of the general cat population are non-white cats (i.e., not pure white), and congenital deafness is extremely rare in non-white cats. However, among white cats, approximately \(75 \%\) with two blue eyes are deaf, \(40 \%\) with one blue eye are deaf, and only \(19 \%\) with eyes of other colors are deaf. Additionally, among white cats, approximately \(23 \%\) have two blue eyes, \(4 \%\) have one blue eye, and the remainder have eyes of other colors. 9 (a) Draw a tree diagram for selecting a white cat (outcomes: one blue eye, two blue eyes, or eyes of other colors) and deafness (outcomes: deaf or not deaf). (b) What is the probability that a randomly chosen white cat is deaf?

Universal blood donors. People with type O-negative blood are referred to as universal donors, although if you give type O-negative blood to any patient, you run the risk of a transfusion reaction due to certain antibodies present in the blood. However, any patient can receive a transfusion of O-negative red blood cells. Only \(7.2 \%\) of the American population have O-negative blood. If 10 people appear at random to give blood, what is the probability that at least one of them is a universal donor?

Playing the slots. Slot machines are now video games, with outcomes determined by random number generators. In the old days, slot machines were like this: you pull the lever to spin three wheels; each wheel has 20 symbols, all equally likely to show when the wheel stops spinning; the three wheels are independent of each other. Suppose that the middle wheel has nine cherries among its 20 symbols, and the left and right wheels have one cherry each. (a) You win the jackpot if all three wheels show cherries. What is the probability of winning the jackpot? (b) There are three ways that the three wheels can show two cherries and one symbol other than a cherry. Find the probability of each of these ways. (c) What is the probability that the wheels stop with exactly two cherries showing among them?