What is the probability that the wafer is from Lot B and is nonconforming

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A population of 598 semiconductor wafers contains wafers from three lots. The wafers are categorized by lot and by whether they conform to a thickness specification, with the results shown in the following table. A wafer is chosen at random from the population. Write your answer as a fraction or a decimal, rounded to four decimal places.

Lot      Conforming       Nonconforming

A              89                        15

B             170                       35

C             261                       28

(a) What is the probability that the wafer is from Lot B?

(b) What is the probability that the wafer is nonconforming?

(c) What is the probability that the wafer is from Lot B and is nonconforming?

(d) Given that the wafer is from Lot B, what is the probability that it is nonconforming?

(e) Given that the wafer is nonconforming, what is the probability that it is from Lot B?

(f) Let E1 be the event that the wafer comes from Lot B, and let E2 be the event that the wafer is nonconforming. Are and independent? An investor is considering a $10,000 investment in a start-up company. She estimates that she has a probability of 0.40 of a $12,200 loss, probability of 0.23 of a $6700 profit, probability of 0.12 of a$56000 profit, and0.25 probability of breaking even ($0 a profit of ). What is the expected value of the profit? Would you advise the investor to make the investment? The expected value of the profit is?

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