A lot of 200 semiconductor chips is inspected by selectingfive at random without

Question

A lot of 200 semiconductor chips is inspected by selectingfive at random without replacement. If at least one of thefive is defective, the lot is rejected. Find the probabilityof rejecting the lot if in the 200,
a) Zero are dective b) 10 are defective c) 20 are defective A lot of 200 semiconductor chips is inspected by selectingfive at random without replacement. If at least one of thefive is defective, the lot is rejected. Find the probabilityof rejecting the lot if in the 200,
a) Zero are dective b) 10 are defective c) 20 are defective

Explanation / Answer

a) 0 since nothing can be rejected. b) This is a hypergeometric distribution with total drawn n = 5,total N = 200, and number of defects m = 10. The PMF for the distribution is given by this formula: http://wiki.stat.ucla.edu/socr/uploads/math/c/b/5/cb5d026b3f4422acf6f769a87ce610fa.png Since we want the case where k = 0 (no defective productsselected), we plug in the previous equation with the numbersspecified to get P(X = 0) = 0.7717. The probability of rejecting the lot, that is 1 - P(X = 0) = 1 -0.7717 = 0.2283 c) Similarly, this is the hypergeometric with total drawn n = 5,total N = 200, and number of defects m = 20. 1 - P(X = 0) = 1 - 0.5872 = 0.4128

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