Question

If a procedure meets all of the conditions of a binomial distribution except the number of trials is not​ fixed, then the geometric distribution can be used. The probability of getting the first success on the xth trial is given by ​P(x)=p(1-p)^x-1​, where p is the probability of success on any one trial. Subjects are randomly selected for a health survey. The probability that someone is a universal donor​ (with group O and type Rh negative​ blood) is 0.07. Find the probability that the first subject to be a universal blood donor is the eighth person selected.

Answer 1

P(first success on x^th trial) = p(1-p)^x-1

P(universal donor), p = 0.07

P(first subject to be a universal blood donor is the eighth person selected) = 0.07 x (1-0.07)^8-1

= 0.04212