Question 888341: A bank’s head office is concerned about the accuracy of the reports being submitted by the bank’s newest branch. The head office observes that 10% of reports from the newest branch contain an error.
During a given week, the head office receives 5 reports from the newest branch. What is the probability that exactly one contains an error? What is the probability that at least one contains an error?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A bank’s head office is concerned about the accuracy of the reports being submitted by the bank’s newest branch. The head office observes that 10% of reports from the newest branch contain an error.
During a given week, the head office receives 5 reports from the newest branch.
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Binomial Problem with n = 5 and p(error) = 0.1
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What is the probability that exactly one contains an error?
P(x = 1) = 5C1*0.1*0.9^4 = binompdf(5,0.1,1) = 0.3281
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What is the probability that at least one contains an error?
P(at least one) = 1 - P(none)
P(at least one) = 1 - P(x = 0) = 1 - 0.9^5 = 0.6126
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Cheers,
Stan H.
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