Let X be the random variable that denotes the number of defective printers in the sample.
A shipment of 10 printers contains 4 that are defective. Therefore, N = 10 and M = 4.
A sample of size 4 is drawn. Therefore, n = 4.
X Hypergeometric (N = 10, M = 4, n = 4)
The pmf of X is
P(X = x) = (MCx * N - MCn - x) / NCn ; x = 0, 1, ......, min(M, n).
= 0 ; otherwise
So, the pmf of X is
P(X = x) = (4Cx * 6C4 - x) / 10C4 ; x = 0, 1, 2, 3, 4.
= 0 ; otherwise
P(X = 0) = (4C0 * 6C4 - 0) / 10C4
= 1 / 14
Therefore, the probability that the sample will not contain a defective printer is 1/14.
A shipment of 10 printers contains 4 that are defective. Find the probability that a sample...
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