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.

Flaws in a certain type of drapery material appear on the average of 3 in 100 square feet. If we assume a Poisson distribution, find the probability of at most one flaw appearing in 250 square feet.

The probability that a company’s workforce has no accidents in a given month is 0.9. The numbers of accidents from month to month are independent. What is the probability that the third month in a year is the first month that at least one accident occurs? What is the probability that the fourth month in a year is the second month that at least one accident occurs?

There are 9 chips in a ball. 3 of them have number 1, 2 of them have number 2, and the rest has number 3. If one chip is selected at random, and the number X (X is either 1, 2 ,or 3) is recorded, what is the expected value of X? what is the variance of X?

For each question on a multiple-choice test, there are four possible answers, of which exactly one is correct. If a student selects answers at random, give the probability that the first question answered correctly is question 3.

Customers arrive at a travel agency at a mean rate of 9 per hour. Assuming that the number of arrivals per hour has a Poisson distribution, give the probability that at least two customers arrive in a given hour.

When a customer buys a product at a supermarket, there is a concern about the item being underweight. Suppose there are 20 “one-pound” packages of frozen ground turkey on display and three of them are underweight. A consumer group buys five of the 20 packages at random. What is the probability that at least one of the five is underweight?