In a clinical study, volunteers are tested for a gene that has been found to increase the risk for a disease. The probability that a person carries the gene is 0.1. (a) If a group of people is tested for the gene, what is the probability that the first one detected with the gene is the 5th one tested? (b) What is the probability that four or more people will have to be tested before one with the gene is detected? If Y is the number of the first person to carry the gene, find (c) E(Y ) and (d) V (Y ).