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)equalsp (1 minus p )Superscript x minus 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 seventh person selected. The probability is nothing. ​(Round to four decimal places as​ needed.)

Answer 1

Answer:

Given p = 0.07 as the probability that someone is a universal donor

In case of Geometric Distribution, Probability of  getting the first success on nth trial is given by

$P (X=n) = p (1-p) ^ {n-1}$

where p is the probability of success on any one trial and (1-p) shows the probability of failure.

So the probability of the first subject to be a universal blood donor will be the seventh person is

$P (X=7) = 0.07 (1-0.07) ^ {7-1} = 0.07 (0.93) ^ 6 = 0.07*0.647 = 0.0453$

So the final probability is 0.0453