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# The probability of a manufacturing company producing a defective item

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Math Expert
Joined: 02 Sep 2009
Posts: 65194
The probability of a manufacturing company producing a defective item  [#permalink]

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02 Jun 2020, 07:44
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55% (hard)

Question Stats:

38% (02:23) correct 62% (01:56) wrong based on 21 sessions

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The probability of a manufacturing company producing a defective item is 0.1. If 5 items are drawn at random from a set of 100 distinct items, without replacement, what is the probability that at least 2 items would be defective?

A. $$1-0.9^4 * 1.4$$

B. $$1-0.9^4$$

C. $$1-0.9^5$$

D. $$1-0.9^4 * 0.5$$

E. $$1-0.9^4* 0.1$$

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The probability of a manufacturing company producing a defective item  [#permalink]

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02 Jun 2020, 07:59
Bunuel wrote:
The probability of a manufacturing company producing a defective item is 0.1. If 5 items are drawn at random from a set of 100 distinct items, without replacement, what is the probability that at least 2 items would be defective?

A. $$1-0.9^4 * 1.4$$

B. $$1-0.9^4$$

C. $$1-0.9^5$$

D. $$1-0.9^4 * 0.5$$

E. $$1-0.9^4* 0.1$$

Probability of a defective item = 0.1
Probability of a NON-defective item = 1-0.1 = 0.9

i.e. Total defective items in 100 items = 10

Probability of atleast 2 defective items = 1- (Probability of no item defective + Probability of 1 item defective)
Probability of atleast 2 defective items = = $$1-(0.9^5+5C4*0.9^4*0.1)$$ = $$1-(0.9^4(0.9+0.5) - 1-0.9^4*1.4$$

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Re: The probability of a manufacturing company producing a defective item  [#permalink]

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02 Jun 2020, 08:33
IMO A

Probability of defective item = 0.1
Probability of non-defective item = 1-0.1= 0.9

Probability of atleast 2 defective items = 1- (Probability of no item defective + Probability of 1 item defective)
= 1- ( (0.9)^5 + 5*(0.1) (0.9)^4) ---- Multiplied by 5 as (DNNNN, NDNNN, NNDNN, NNNDN, NNNND)
= 1- (0.9^4)* (0.9 + 0.5)
= 1-(0.9^4) * 1.4
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The probability of a manufacturing company producing a defective item  [#permalink]

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02 Jun 2020, 08:53
Bunuel wrote:
The probability of a manufacturing company producing a defective item is 0.1. If 5 items are drawn at random from a set of 100 distinct items, without replacement, what is the probability that at least 2 items would be defective?

A. $$1-0.9^4 * 1.4$$

B. $$1-0.9^4$$

C. $$1-0.9^5$$

D. $$1-0.9^4 * 0.5$$

E. $$1-0.9^4* 0.1$$

Given: The probability of a manufacturing company producing a defective item is 0.1.
Asked: If 5 items are drawn at random from a set of 100 distinct items, without replacement, what is the probability that at least 2 items would be defective?

The probability of a manufacturing company producing a defective item is 0.1
The probability of a manufacturing company producing a non-defective item is 0.9

The probability that at least 2 items would be defective = 1- Probability of (0 item defective) - Probability of(1 item defective) = 1 - .9^5 - 5C1*(.1)(.9)^4 = 1 - .9^4 (.9 + .5) = 1 - .9^4*1.4

IMO A
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The probability of a manufacturing company producing a defective item   [#permalink] 02 Jun 2020, 08:53