1) A procedure often used to control the quality of name-brand food products utilizes a panel offive"tasters." Each member of the panel tastes three samples, two of which are from batches of the product known to have the desired taste and the other from the latest batch. Each taster selects the sample that is different from the other two. Assume that the latest batch does have the desired taste, and that there is no communication between the tasters.

(a)

If the latest batch tastes the same as the other two batches, what is the probability that the taster picks it as the one that is different? (Enter your probability as a fraction.)

(b)

What is the probability that exactlythreeof the tasters picks the latest batch as different? (Round your answer to three decimal places.)

(c)

What is the probability that at least one of the tasters picks the latest batch as different? (Round your answer to three decimal places.)

2) Consider a Poisson random variable with=0.8. UseTable 2in Appendix I to find the following probabilities. (Round your answers to three decimal places.)

P(2x4) =

3) Consider a binomial random variable withn=5andp=0.7.Letxbe the number of successes in the sample. (Round your answers to three decimal places.)

FindP(3x4).=