A lot of 25 items is to be inspected by means of a two-stage sampling plan. A sa

Question

A lot of 25 items is to be inspected by means of a two-stage sampling plan. A sample of five items is drawn. If one or more is bad, the lot is rejected. If all are nondefective, a second sample of 10 items is drawn from the remaining 20 items. The lot is then rejected if any item in the second sample is bad; otherwise it is accepted. Find the probability of accepting a lot which has two defective items. An alternative single-stage plan for this problem might be to choose a single sample of 15 items and accept the lot only if there are no defectives in the sample. Find the probability of accepting a lot of 25 with two defectives and compare this probability with that found in (a). (a) (b)

Explanation / Answer

P(defective item ) = 2 /25

a) P( accepting an lot) = P(selecting 5 non defective items out of 23 non defective items) *P(selecting 10 non defective items out of 18 non defective items)

=C(23,5)/C(25,5)*C(18,10)/C(20,10)

=33649/53130*43758/184756

=0.63*0.23 =0.145

b) P( accepting an lot) = P(selecting 15 non defective items out of 23 non defective items)

=C(23,15)/C(25,15)

=490314/3268760 = 0.15

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