There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item ?

Solution

Here $straight p space equals 5 over 100 space equals 1 over 20 comma space space straight q space equals space 1 minus straight p space equals space 1 minus 1 over 20 space equals space 19 over 20 comma space space straight n space equals space 10$
Required probability = P(no defective) + P(1 defective)
$equals space straight C presuperscript 10 subscript 0 space open parentheses 19 over 20 close parentheses to the power of 10 space plus space straight C presuperscript 10 subscript 1 space open parentheses 19 over 20 close parentheses to the power of 9 space open parentheses 1 over 20 close parentheses to the power of 1 equals space 1 space cross times space open parentheses 19 over 20 close parentheses to the power of 10 plus space 10 over 1 cross times open parentheses 19 over 20 close parentheses to the power of 9 cross times 1 over 20 space equals open parentheses 19 over 20 close parentheses to the power of 19 space open square brackets 19 over 20 plus 10 over 20 close square brackets space equals open parentheses 19 over 20 close parentheses to the power of 9 space cross times 29 over 20$

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Probability

There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item ?

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