Question

1) a) A drawer contains 9 white socks and 7 black socks. Two different socks are selected from the drawer at random. What is the probability that both of the selected socks are white?

b) A box contains 10 white marbles and 7 black marbles. Suppose we randomly draw a marble from the box, replace it, and then randomly draw another marble from the box. (This means that we might observe the same marble twice). What is the probability that both the marbles are white?

c) Suppose that 3.4 % of the items produced by a factory are defective. If 5 items are chosen at random, what is the probability that none of the items are defective?

d) Suppose that 5.7 % of the items produced by a second factory are defective. If 5 items are chosen at random from the second factory, what is the probability that exactly one of the items is defective?

2) a) Suppose that 8.8 % of the items produced by a third factory are defective. If 5 items are chosen at random from the third factory, what is the probability that exactly two of the items are defective?

b) Suppose that 5.1 % of the items produced by a fourth factory are defective. If 5 items are chosen at random from the fourth factory, what is the probability that at least two of the items are defective?

c) Suppose that 9.6 % of the items produced by a fifth factory are defective. If 6 items are chosen at random from the fifth factory, what is the expected value (or mean value) for the number of defective items?

d) In a certain town, 19 % of the population develop lung cancer. If 25 % of the population are smokers and 85% of those developing lung cancer are smokers, what is the probability that a smoker in this town will develop lung cancer?

e) . A certain kind of light bulb has a 8.5 percent probability of being defective. A store receives 54 light bulbs of this kind. What is the expected value (or mean value) of the number of light bulbs that are expected to be defective?

Answer 1