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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.

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

P(not more than 2 defective items) = P(0) + P(1) + P(2)
$equals space straight C presuperscript 5 subscript 0 space open parentheses 19 over 20 close parentheses to the power of 5 space plus space straight C presuperscript 5 subscript 1 space open parentheses 19 over 20 close parentheses to the power of 4 space open parentheses 1 over 20 close parentheses space plus space straight C presuperscript 5 subscript 2 space open parentheses 19 over 20 close parentheses cubed space open parentheses 1 over 20 close parentheses squared equals space open parentheses 19 over 20 close parentheses cubed space open square brackets straight C presuperscript 5 subscript 0 cross times open parentheses 19 over 20 close parentheses squared space plus space straight C presuperscript 5 subscript 1 space cross times space open parentheses 19 over 20 close parentheses space cross times space open parentheses 1 over 20 close parentheses space plus space straight C presuperscript 5 subscript 2 cross times open parentheses 1 over 20 close parentheses squared close square brackets equals space open parentheses 19 over 20 close parentheses cubed space open square brackets 1 space cross times space 361 over 400 plus space 5 over 1 cross times 19 over 400 plus fraction numerator 5 space cross times space 4 over denominator 1 space cross times 2 end fraction cross times 1 over 400 close square brackets space equals open parentheses 19 over 20 close parentheses cubed space open parentheses fraction numerator 361 plus 45 plus 10 over denominator 400 end fraction close parentheses space equals open parentheses 19 over 20 close parentheses cubed space cross times space 466 over 400 space equals open parentheses 19 over 20 close parentheses cubed space cross times 233 over 200$

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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?

95 Views

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?

91 Views

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.

85 Views