Question

A retailer inspects a sample of 25 wooden blankets from a lot of 500 blankets he purchased every week and returns the lot to the manufacturer if there are more than 2 defective blankets in the sample. If a lot of 40 defective bl;ankets is purchased by the retailer, what is probability that it will be rejected and returned to the manufacturer> What is the chance of accepting the lot?

Answer 1

Combination formula for selecting r items from n, nCr = n!/(r! x (n-r)!)

Total number of blankets = 500

Number of defective blankets = 40

Number of non defective blankets = 500 - 40 = 460

P(accepting the lot) = P(2 or less defective blankets)

= P(0 defective blankets) + P(1 defective blanket) + P(2 defective blankets)

= 460C25/500C25 + (40C1 x 460C24)/500C25 + (40C2 x 460C23)/500C25

= 0.1178 + 0.2702 + 0.2894

= 0.6774

P(rejected and returned to manufacturer) = 1 - P(accepting the lot)

= 1 - P(2 or less defective blankets)

= 1 - 0.6774

= 0.3226