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1001. The items produced by a company contain 5% defective items. Show that the probability of getting 2 defective items in a sample of 10 items is $fraction numerator 45 space cross times space 19 to the power of 8 over denominator 20 to the power of 10 end fraction.$

Here n = 10
$straight p space equals space 5 over 100 space equals 1 over 20 comma space space straight q space equals space 1 space minus space straight p space equals 1 space minus 1 over 20 space equals space 19 over 20$

Required probability = $straight P left parenthesis 2 right parenthesis space equals space straight C presuperscript 10 subscript 2 space open parentheses 19 over 20 close parentheses to the power of 8 space open parentheses 1 over 20 close parentheses squared$

$equals space fraction numerator 10 space cross times space 9 over denominator 1 space cross times 2 end fraction cross times 19 to the power of 8 over 20 to the power of 8 cross times 1 over 20 squared space equals fraction numerator 45 space cross times space 19 to the power of 18 over denominator 20 to the power of 10 end fraction$

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1002. 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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1003. A bag consists of 10 balls each marked with one of the digits 0 to 9. If four balls are drawn successively with replacement from the bag, what is the probability that none is marked with the digit 0?

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1004. On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?

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1005. 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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1006. The items produced by a firm are supposed to contain 5% defective items. What is the probability that a sample of 8 items will contain less than 2 defective items?

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1007. There are 5% defective items in large bulk of items. Find the probability that a sample of 5 items will include not more than 2 defective items.

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1008. 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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1009. The items produced by a firm are supposed to contain 5% defective items. What is the probability that a sample of 8 items will contain less than 2 defective items?

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Long Answer Type

1010. There are 8 % defective items in a large bulk of items. Find the probability that a sample of 10 items will include not more than 3 defective items.