SOLUTION: An assembly line puts widgets together with a success rate of 95%. ( i.e. 5% of the widgets are defective. ) A quality control inspector selects widgets and tests them one at a

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Question 767081:
An assembly line puts widgets together with a success rate of 95%. ( i.e. 5% of the widgets are defective. ) A quality control inspector selects widgets and tests them one at a time. If 10 widgets are tested, find the probability that no more than 1 widget will be defective.
Answer by reviewermath(1029) About Me  (Show Source):
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Q:
An assembly line puts widgets together with a success rate of 95%. ( i.e. 5% of the widgets are defective. ) A quality control inspector selects widgets and tests them one at a time. If 10 widgets are tested, find the probability that no more than 1 widget will be defective.
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X = number of defective widgets
X ~ Binomial(10, 0.05)
P(X ≤ 1) = %28matrix%282%2C1%2C10%2C0%29%29%280.05%5E0%29%280.95%5E10%29 + %28matrix%282%2C1%2C10%2C1%29%29%280.05%5E1%29%280.95%5E9%29 = highlight%280.91386%29