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Probability

Short Answer Type

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.

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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.

Here n = 10
$straight p space equals 8 over 100 space equals 2 over 25 comma space space space straight q space equals space 1 space minus space straight p space equals space 1 minus 2 over 25 space equals space 23 over 25$

P(not more than 3 defective items) = P(0) + P(1) + P(2) + P(3)
$equals space straight C presuperscript 10 subscript 0 open parentheses 23 over 25 close parentheses to the power of 10 space plus space straight C presuperscript 10 subscript 1 space open parentheses 2 over 25 close parentheses space open parentheses 23 over 25 close parentheses to the power of 9 space plus space straight C presuperscript 10 subscript 2 space open parentheses 2 over 25 close parentheses squared space open parentheses 23 over 25 close parentheses to the power of 8 space plus space straight C presuperscript 10 subscript 3 space open parentheses 2 over 25 close parentheses cubed space open parentheses 23 over 25 close parentheses to the power of 7 equals space 1 space cross times space open parentheses 23 over 25 close parentheses to the power of 10 space plus space 10 over 1 cross times 2 over 25 cross times space open parentheses 23 over 25 close parentheses to the power of 9 space plus space fraction numerator 10 space cross times 9 over denominator 1 cross times 2 end fraction cross times space open parentheses 2 over 25 close parentheses squared space cross times open parentheses 23 over 25 close parentheses to the power of 8 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space plus space fraction numerator 10 cross times 9 cross times 8 over denominator 1 cross times 2 cross times 3 end fraction open parentheses 2 over 25 close parentheses cubed space space open parentheses 23 over 25 close parentheses to the power of 7 equals space open parentheses 23 over 25 close parentheses to the power of 7 space open square brackets open parentheses 23 over 25 close parentheses cubed plus 4 over 5 cross times open parentheses 23 over 25 close parentheses squared space plus space 45 space cross times space open parentheses 2 over 25 close parentheses squared space cross times 23 over 25 plus 120 space cross times space open parentheses 2 over 25 close parentheses cubed close square brackets equals space fraction numerator left parenthesis 23 right parenthesis to the power of 7 over denominator left parenthesis 25 right parenthesis to the power of 10 end fraction space open square brackets left parenthesis 23 right parenthesis squared plus space 20 space cross times space left parenthesis 23 right parenthesis squared space plus space 45 space cross times space 4 space cross times 23 space plus 120 space cross times 8 close square brackets equals space fraction numerator left parenthesis 23 right parenthesis to the power of 7 over denominator left parenthesis 25 right parenthesis to the power of 10 end fraction left square bracket 12167 space plus space 10580 space plus space 4140 space plus space 960 right square bracket space equals space 27847 space open square brackets fraction numerator left parenthesis 23 right parenthesis to the power of 7 over denominator left parenthesis 25 right parenthesis to the power of 10 end fraction close square brackets$

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