Startlebucks, a local Michigan coffee supplier, receives coffee beans from both

Question

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 3. 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

Total % of unacceptable Sumatran beans in the mix = 0.05*0.3 = 0.015

Total % of unacceptable Ethiopian beans in the mix = 0.1*0.7 = 0.07

P(unacceptable bean from Ethopia ) = 0.07/(0.07+0.015) = 0.82

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