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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?

Here n = 45
p = P (ball drawn is marked with 0) = $1 over 10$

$left parenthesis because space only space one space ball space out space of space 10 space is space marked space with space 0 right parenthesis$

$therefore space space space straight q space equals space 1 minus straight p space equals space 1 minus 1 over 10 space equals 9 over 10$
P(none is marked with the digit 0) = P(0) = $straight C presuperscript 4 subscript 0 space open parentheses 9 over 10 close parentheses to the power of 4$

$equals space 1 space cross times space open parentheses 9 over 10 close parentheses to the power of 4 space equals space open parentheses 9 over 10 close parentheses to the power of 4 space equals 6561 over 10000.$

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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.

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