(-) (+) 95% , A lot of 12 parts contain 3 defective parts. Assume sampling witho

Question

(-) (+) 95% , A lot of 12 parts contain 3 defective parts. Assume sampling without replacement. (a) What is the probability that 1 defective part will be found in a sample of 3. size 4? (b) What is the probability that at least one defective part will be drawn in a sample of size of size 4? If three parts are selected and you know the first two parts were defective, what is the probability that the 3rd part drawn will also be defective? (c) (d) A sample of size four is taken and each part drawn is recorded as being either good or defective and then replaced back in the lot and mixed before the next draw. What is the probability that at least one part in the four draws will be defective? 6.75 x 8.60 in

Explanation / Answer

3.

(a) P(X=1) = 4C1 * (3C1/12C1) * (9C3/11C3) = 4 * 0.25 * 0.5091 = 0.5091

(b) P(X>=1) = 1 - P(X < 1)
P(X < 1) = 9C4/12C4 = 126/495 = 0.2546
P(X >= 1 ) = 1 - 0.2546 = 0.7455

(c)
Probability that first two parts are defective, P(A) = 3/12 * 2/11 * (1/10 + 9/10) = 0.0455

Probability that all 3 parts are defective, 3C3/12C3 = 0.0045

P(B|A) = P(A and B)/P(A) = 0.0045/0.0455 = 0.0989

(d)
p = 3/12 = 0.25
P(X>=1) = 1 - P(X < 1)
P(X < 1) = (1-p)^4 = 0.75^4 = 0.3164

P(X>=1) = 1 - 0.3164 = 0.6836

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