If a procedure meets all of the conditions ofa geometric distribution can be use

Question

If a procedure meets all of the conditions ofa geometric distribution can be used. The probability of getting the first success on the xth trial is given by 11. P(x)-p/1-p1, 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 0.14. Find the probability that the first subject to be a universal blood donor is the eighth person selected. The probability is (Round to four decimal places as needed.)

Explanation / Answer

Getting the first success on the 'x' trail : P(x)= p(1-p)x-1

For the given problem,

Probability that the first subject to be a universal donor is the eighth person selected.

Success : subject to be a universal donor.

p : Probability of success : Probability that someone is a universal donor = 0.14

x=8 ; first success in 8th trail, i.e first subject to be a universl donor is the eighth person selected

Plugging the values x=8 and p=0.14 in the equation

P(x)= p(1-p)x-1

P(8) = 0.14 x (1-0.14)8-1 = 0.14 x 0.867 = 0.0487

Probability that the first subject to be a universal donor is the eighth person selected = 0.0487

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