A warranty is written on a product worth $10,000 so that the buyer is given $8000 if it fails in the first year, $6000 if it fails in the second, and zero after that. The probability of the product’s failing in a year is 0.15; failures are independent of those of other years. What is the expected value of the warranty?

The probability that a machine produces a defective item is 0.02. Each item is checked as it is produced. Assume that these are independent trials, and compute the probability that at least 90 items must be checked to find one that is defective.

Bowl A contains 3 white and 2 red chips, bowl B contains 4 white and 4 red chips, and bowl C contains 4 white and 5 red chips. The probabilities of selecting bowls A, B, and C are 1/3, 1/6, and 1/2 respectively. One chip is selected at random. Given that a white chip is selected what is the probability that it came from bowl C. Round your answer to three decimal places.