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You are here: Experts > Science > Mathematics > Advanced Math > Probability
Expert: Chen Min
Date: 5/18/2008
Subject: Probability
Question
The owners of Superb Coffee want to buy 100 bags of coffee from Great Aroma. They take a sample of 10 bags and agree to buy the consignment if, at most, 1 bag in the sample fails to meet their exacting quality requirement. Great Aroma knows that 10% of the total consignment will not meet their requirements. What is the probability that they will buy the consignment?
Answer
There are ten bags that are not able to meet the requirements
Atmost one bag can be in the samples
Circumstance one: All the samples they take meet their demands
10 10
P1 = C / C
90 100
= 90!*10!(100-10)!/100!*10!(90-10)!
= 90!90!/80!100!
= 81*82*83*84*...*90/91/92/93/..../100
= 0.33
Circumstance two: One bad bag is taken:
9 1 10
P2 = C *C / C
90 10 100
= 90!90!10!10!/9!9!81!100!
= 90!90!/80!100! *100/81
= 0.33 * 100/81
= 0.41
Therefore the probability that they would buy the consignment is
P1+P2 = 74%
Hope this helps:)
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