1. Suppose that the probability of having an accident-free day at a power plant is 60%. Assume all days are independent of each other. The plant manager wants to determine the likelihood of various numbers of accident-free days occurring over the course of a week

. a) Define a random variable for this problem and state its distribution and parameters.

b) Find the probability that there are 3 days accident-free days in one week.

c) Find the probability that at least 2 accident-free days in one week.

d) Find the probability that there will be 5 days with accidents in one week.

e) Find the probability that there are at least 4 days with accidents in one week.

4. To save time and money when testing blood samples for the presence of a disease, the following procedure is sometimes used: Blood samples from a number of people are pooled together and the pooled sample is tested. If the pooled sample is negative, then no further testing needs to be done. If the pooled sample is positive, however, then each one of the separate samples must be tested individually. To be specific, suppose that the blood samples of 10 people are pooled together in this procedure, and suppose that the proportion of those who have the disease in the population from which the samples are drawn is 0.02. (Also assume that the presence of the disease in one sample is independent of the presence of the disease in the other samples.)

a) Find the probability that the pooled sample is negative.

b) Let X be the number of tests that must be run. Construct the probability distribution of X.

c) Compute the average number of tests that need to be run using this method of pooling samples. Is the method of testing 10 people at once better than testing each person separately?