1a) Factories A, B, and C produce computers. Factory A produces 4 times as many computers as factory C, and factory B produces 7 times as many computers as factory C. The probability that a computer produced by factory A is defective is 0.026, the probability that a computer produced by factory B is defective is 0.035, and the probability that a computer produced by factory C is defective is 0.034.
A computer is selected at random and it is found to be defective. What is the probability it came from factory B?
1b) A new medical test has been designed to detect the presence of the mysterious Brainlesserian disease. Among those who have the disease, the probability that the disease will be detected by the new test is 0.82. However, the probability that the test will erroneously indicate the presence of the disease in those who do not actually have it is 0.04. It is estimated that 10% of the population who take this test have the disease.
If the test administered to an individual is positive, what is the probability that the person actually has the disease?
1c) In a random sample of 1,000 people, it is found that 8.2% have a liver ailment. Of those who have a liver ailment, 7% are heavy drinkers, 60% are moderate drinkers, and 33% are nondrinkers. Of those who do not have a liver ailment, 9% are heavy drinkers, 47% are moderate drinkers, and 44% are nondrinkers.
If a person is chosen at random, and he or she is a heavy drinker, what is the empirical probability of that person having a liver ailment?
1d) A biomedical research company produces 49% of its insulin at a plant in Kansas City, and the remainder is produced at a plant in Jefferson City. Quality control has shown that 0.95% of the insulin produced at the plant in Kansas City is defective, while 0.75% of the insulin produced at the plant in Jefferson City is defective. What is the probability that a randomly chosen unit of insulin came from the plant in Jefferson City given that it is defective?
