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Question

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


A

272019207

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B

53340019206

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C

153201207

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D

35161206

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Solution

The correct option is A

272019207


Explanation for the correct option:

Find probability using the binomial probability theorem.

  • Given: The probability of items supposed to have defected is 5%.
  • Sample of 8 items and 2 of them are defective.
  • Let the number of defective items be x. so, x=2.
  • Let P be the probability of getting a defective item and P is 5%. So, P=5100.

Assume that, q is the probability of containing undefeated items.

We know that the sum of probability is 1.

So,

q=1-pq=1-5100q=95100

For P(x<2) assume that P1 be the probability that a sample of 8 items will contain less than 2 defective item.

P1=P(x=0)+P(x=1)P1=C0851000951008+C1851001951007P1=C08120019208+C18120119207P1=19208+8×120×19207P1=192071920+820P1=192072720

Therefore, the required probability is 192072720.

Hence, the probability that a sample of 8 items will contain less than 2 defective item is 192072720.


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