Question

There are 6% defective items in a large bulk of items. Find the probability that a sample of 8 items will include not more than one defective item?

Solution

Here n = 8
$straight p space equals space 6 over 100 space equals space 3 over 50 comma space space space straight q space equals space 1 space minus space straight p space equals space 1 minus 3 over 50 space equals space 47 over 50$
P(not more than one defective item) = P(0) + P(1)
$equals space straight C presuperscript 8 subscript 0 space open parentheses 47 over 50 close parentheses to the power of 8 plus space straight C presuperscript 8 subscript 1 space open parentheses 47 over 50 close parentheses to the power of 7 space open parentheses 3 over 50 close parentheses space equals open parentheses 47 over 50 close parentheses to the power of 7 space open square brackets 1 space cross times space 47 over 50 plus 24 over 50 close square brackets space equals space open parentheses 47 over 50 close parentheses to the power of 7 space cross times 71 over 50$

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Probability

There are 6% defective items in a large bulk of items. Find the probability that a sample of 8 items will include not more than one defective item?

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