Question

A car dealership selects 3 cars at random (n). If a total of 13cars(N) are in the lot and 5 of those cars are defective (D), what is the hypergeometric probability of the dealership getting 0 defective cars (x) in its selection?

a. 3.5%
b. 72.0%
c. 28.0%
d. none of the other answers
e. 19.6%
f.49.0%

Answer 1

The hypergeometric probability of the dealership getting 0 defective cars in its selection from 13 cars with 5 defective ones is 19.6%, which corresponds to answer choice e.

Step-by-step explanation:

The subject of the question is hypergeometric probability, which is used to calculate the probability of a given number of successes in a sample drawn without replacement. To find the hypergeometric probability of the dealership getting 0 defective cars (x) when selecting 3 cars at random (n) from a total of 13 cars (N) with 5 defective ones among them (D), we use the formula:

P(X = x) = [(C(D, x) * C(N-D, n-x))] / C(N, n)

Plugging in the values:

P(X = 0) = [(C(5, 0) * C(13-5, 3-0))] / C(13, 3)

P(X = 0) = [(1 * C(8, 3))] / C(13, 3)

P(X = 0) = [(1 * 56)] / 286

P(X = 0) = 56 / 286

P(X = 0) = 0.1958 or 19.6%

Hence, the correct answer is e. 19.6%.