3. Startlebucks, a local Michigan coffee supplier, receives coffee beans from bo

Question

3. Startlebucks, a local Michigan coffee supplier, receives coffee beans from both Ethiopia and Sumatra. The Sumatra source generally has 5% of its beans found to be unacceptable, while the more expensive but popular Ethiopia beans come from a source that has 10% of beans deemed unacceptable. Thirty percent of Startlebucks "Elite Wakeup"mix of coffee comes from Sumatra. If a bean is selected at random from inventory and it is found to be unacceptable, what is the probability that that bean came from Ethiopia?

Explanation / Answer

P( Sumatra )=0.3

P( unacceptable | Sumatra)=0.05

P( Ethopia)=1-0.3=0.7

P( unacceptable |Ethopia)=0.1

Thus P(unaccepatble)=P( unacceptable | Sumatra)*P(Sumatra)+P(unacceptable |Ethopia)*P( Ethopia) = 0.05*0.3+0.1*0.7=0.085

P(Ethopia | unacceptable)=P(unacceptable|Ethopia)*P(Ethopia)/P(unacceptable)=0.1*0.7/0.085=0.82353

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