It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles, 9 are defective?

Solution

Here n = 12
$straight p space equals space 10 over 100 space equals 1 over 10 comma space space straight q space equals space 1 minus straight p space equals space 1 minus 1 over 10 space equals space 9 over 10$
$straight P left parenthesis 9 space articles space are space defective right parenthesis space equals space straight P left parenthesis 9 right parenthesis space equals space straight C presuperscript 12 subscript 9 space open parentheses 9 over 10 close parentheses cubed space open parentheses 1 over 10 close parentheses to the power of 9 space$
$equals space straight C presuperscript 12 subscript 3 space cross times space 9 cubed over 10 cubed cross times 1 over 10 to the power of 9 space equals fraction numerator 12 cross times 11 cross times 10 over denominator 1 cross times 2 cross times 3 end fraction space cross times 9 cubed over 10 to the power of 12 equals space 220 space cross times space 729 over 10 to the power of 12 space equals 160380 over 10 to the power of 12 space equals 16038 over 10 to the power of 11$

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Probability

It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles, 9 are defective?

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