Reference no: EM132858204

a) It is known that CDs produced by a manufacturer will be defective with probability 0.1, independently of each other. A company sells the CDs in packages of size 10 and offers a money-back guarantee if more than 1 of the 10 CDs in the package will be defective. If someone buys 3 packages, what is the probability that he will return at least one of them?

b) A station has two mini-buses (each with 16 seats), A and B, awaiting, each already having 13 seats occupied. Passengers come singly, selecting A with probability 0.7 and selecting B with probability 0.3. Find the probability that B is filled up before A and moves out first.

c) The number of times that an individual contracts a cold in a given year is a Poisson random variable with parameter λ = 5. Suppose a new wonder drug (based on large quantities of vitamin C) has just been marketed that reduces the Poisson parameter to λ = 3 for 75% of the population. For the other 25% of the population the drug has no appreciable effect on colds. If an individual tries the drug for a year and has 2 colds in that time period, how likely is it that the drug is beneficial for him/her?

d) The probability of being dealt a full house in a hand of poker is approximately 0.0014. Find an approximation for the probability that in 1000 hands of poker you will be dealt at least 2 full houses