CONDITIONAL PROBABILITY 1. A random sample of 200 adults are classified below by sex and their level of education attained. Education Male Female Elementary 38 45 Secondary 28 50 College 22 17 If a person is picked at random from this group, find the probability that (a) the person is a male, given that the person has a secondary education; (b) the person does not have a college degree, given that the person is a female. 2. In an experiment to study the relationship of hypertension and smoking habits, the following data are collected for 180 individuals:
where H and NH in the table stand for Hypertension and Nonhypertension, respectively. If one of these individuals is selected at random, find the probability that the person is (a) experiencing hypertension, given that the person is a heavy smoker; (b) a nonsmoker, given that the person is experiencing no hypertension. 3. The probability that a married man watches a certain television show is 0.4, and the probability that a married woman watches the show is 0.5. The probability that a man watches the show, given that his wife does, is 0.7. Find the probability that (a) a married couple watches the show; (b) a wife watches the show, given that her husband does; (c) at least one member of a married couple will watch the show.
4. For married couples living in a certain suburb, the probability that the husband will vote on a bond referendum is 0.21, the probability that the wife will vote on the referendum is 0.28, and the probability that both the husband and the wife will vote is 0.15. What is the probability that (a) at least one member of a married couple will vote? (b) a wife will vote, given that her husband will vote? (c) a husband will vote, given that his wife will not vote?
BAYES’ RULE 1. In a certain region of the country it is known from past experience that the probability of selecting an adult over 40 years of age with cancer is 0.05. If the probability of a doctor correctly diagnosing a person with cancer as having the disease is 0.78 and the probability of incorrectly diagnosing a person without cancer as having the disease is 0.06, a) what is the probability that an adult over 40 years of age is diagnosed as having cancer? b) what is the probability that a person diagnosed as having cancer actually has the disease? 2. Police plan to enforce speed limits by using radar traps at four different locations within the city limits. The radar traps at each of the locations L1, L2, L3, and L4 will be operated 40%, 30%, 20%, and 30% of the time. If a person who is speeding on her way to work has probabilities of 0.2, 0.1, 0.5, and 0.2, respectively, of passing through these locations, a) what is the probability that she will receive a speeding ticket? b) If the person received a speeding ticket on her way to work, what is the probability that she passed through the radar trap located at L2? BINOMIAL DISTRIBUTION 1. The probability that a patient recovers from a delicate heart operation is 0.9. What is the probability that exactly 5 of the next 7 patients having this operation survive? 2. A traffic control engineer reports that 75% of the vehicles passing through a checkpoint are from within the state. What is the probability that fewer than 4 of the next 9 vehicles are from out of state? 3. A national study that examined attitudes about antidepressants revealed that approximately 70% of respondents believe “antidepressants do not really cure anything, they just cover up the real trouble.” According to this study, what is the probability that at least 3 of the next 5 people selected at random will hold this opinion? 4. It is known that 60% of mice inoculated with a serum are protected from a certain disease. If 5 mice are inoculated, find the probability that (a) none contracts the disease; (b) fewer than 2 contract the disease; (c) more than 3 contract the disease.
