Three machines I, II and III manufacture 30%, 30% and 40%, respectively, of the total output of certain items. Of them, 4%, 3% and 2%, respectively, are defec- tive. One item is drawn at random, tested and found to be defective. What is the probability that the item was manufactured by each one of the machines I, II and III?

Ponderosa Paint and Glass carries three brands of paint. A customer wants to buy another gallon of paint to match paint she purchased at the store previously. She can’t recall the brand name and does not wish to return home to find the old can of paint. So, she selects two of the three brands of paint at random and buys them. What is the probability that she matched the paint brand? Her husband also goes to the paint store and fails to remember what brand to buy. So, he also purchases two of the three brands of paint at random. Determine the probability that both the woman and her husband fail to get the correct brand of paint. (Hint: Are the husband’s selections independent of the wife’s selections?)

Brian, a landscape architect, submitted a bid on each of three home landscaping projects. He estimates that the probabilities of winning the bid on Project A, Project B, and Project C are 0.7, 0.5, and 0.2, respectively. Assume that the probability of winning a bid on one of the three projects is independent of winning or losing the bids on the other two projects. Find the probability that Brian will experience the following. (a) Win all three of the bids (b) Win exactly two of the bids (c) Win exactly one bid

If you have a sample of 100 patients at a hospital and 20 of them have the flu, what is the probability Of randomly selecting 3 patients in a row who have the flue?

Three machines turn out all the products in a factory, with the first machine producing 35% of the products, the second machine 25%, and the third machine 40%. The first machine produces defective products 19% of the time, the second machine 11% of the time and the third machine 3% of the time. What is the probability that a non-defective product came from the second machine? (Round your answer to four decimal places.)

With regards to a particular gene, the percentage of genotypes AA, Aa, and aa in a particular population are respectively, 60%, 30%, and 10%. Furthermore, the percentages of these genotypes that contract a certain disease are respectively. 1%, 5% and 20%. If a person does contract the disease, what is the probability that the person is of genotype AA?

The management of the large department store in Example B.1 must determine whether more training is neededfor the customer service clerk. The clerk at the customer service desk can serve an average of three customersper hour. What is the probability that a customer will require 10 minutes or less of service?