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 0.11. Find the probability that the first subject to be a universal blood donor is the fifth person selected.

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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

0.11.

Find the probability that the first subject to be a universal blood donor is the

fifth

person selected.

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