A hypergeometric probability experiment is conducted with the given parameters. Compute the probability ofobtaining x successes. $$\mathrm { N } = 130 , \mathrm { n } = 10 , \mathrm { k } = 25 , \mathrm { x } = 3$$
A) 0.1965
B) 0.1914
C) 0.1867
D) 0.1722

Question

Quizplus · Accepted Answer

The probability of obtaining x successes in a hypergeometric probability experiment is given by the formula:```P(X = x) = (C(k, x) * C(N-k, n-x)) / C(N, n)```where:* N is the total number of items in the population* n is the number of items drawn from the population* k is the number of successes in the population* x is the number of successes in the sampleIn this case, we have:* N = 130* n = 10* k = 25* x = 3Plugging these values into the formula, we get:```P(X = 3) = (C(25, 3) * C(105, 7)) / C(130, 10) = 0.1965```Therefore, the probability of obtaining 3 successes is 0.1965, which is choice A.

A Hypergeometric Probability Experiment Is Conducted with the Given Parameters N=130,n=10,k=25,x=3\mathrm { N } = 130 , \mathrm { n } = 10 , \mathrm { k } = 25 , \mathrm { x } = 3N=130,n=10,k=25,x=3

A Hypergeometric Probability Experiment Is Conducted with the Given Parameters $\mathrm { N } = 130 , \mathrm { n } = 10 , \mathrm { k } = 25 , \mathrm { x } = 3$