A wholesale distributor for an internet sales company provides replacement mecha

Question

A wholesale distributor for an internet sales company provides replacement mechanical products from a centrally located warehouse. At any given time, the percent of "bad" O-ring seals made by brand "A" is 10%. There are 60 brand "A" O-rings in stock A purchase has come in from five different portable tool manufacturers for one O ring each. What is the probability that three of the orders will ship a bad O-ring? A new batch of rings from brand "B" are now selling along side brand "A". A set of 6 O-rings are being shipped. You happen to know that 4 of the rings are brand "A" while the other 2 are brand "B". Brand "B" has a "bad" rate that is different than brand "A" (and you don't need to know what that rate is to solve this problem). What is the probability that the shipment contains one brand A O-ring that is bad? a. b.

Explanation / Answer

Number of bad O-rings = 60x0.1 = 6

Number of good O-rings = 60-6 = 54

a) p = P(three orders will ship bad O-rings) = 6C3x54C2/60C6

= 20x1431/50,063,860

= 0.0006

b) The probability of an A O-ring being bad is independent of the brand B O-rings

P(one brand A O-ring that is bad in 4) = 6C1x54C3/60C4

= 6x24,804/487635

= 0.3052

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