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A manufacturer is using glass as the surface

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Director
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A manufacturer is using glass as the surface  [#permalink]

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New post 23 Dec 2012, 23:36
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A manufacturer is using glass as the surface for the multi-touch screen of its smartphone. The glass on the manufactured phone has a 5% probability of not passing quality control tests. The quality control manager bundles the smartphone in groups of 10. If that bundle has any smartphone that does not pass the quality control test, the entire bundle of 10 is rejected.

What is the probability that a smartphone bundle that will be rejected by quality control?

(A) 0.25

(B) .05^10

(C) 1-0.95^10

(D) 1-0.05^10

(E) 0.95^10
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Re: A manufacturer is using glass as the surface  [#permalink]

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New post 24 Dec 2012, 00:16
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fozzzy wrote:
A manufacturer is using glass as the surface for the multi-touch screen of its smartphone. The glass on the manufactured phone has a 5% probability of not passing quality control tests. The quality control manager bundles the smartphone in groups of 10. If that bundle has any smartphone that does not pass the quality control test, the entire bundle of 10 is rejected.

What is the probability that a smartphone bundle that will be rejected by quality control?

(A) 0.25

(B) .05^10

(C) 1-0.95^10

(D) 1-0.05^10

(E) 0.95^10


A bundle will be rejected by quality control if at least one phone do not pass the test.

Find the probability of the opposite event and subtract from 1.

The opposite event is that bundle will NOT be rejected by quality control, which will happen if all 10 phones pass the test, so P(all 10 phones pass test)=0.95^10.

P(at least one phone do not pass the test)=1- P(all 10 phones pass test)=1-0.95^10.

Answer: C.
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Director
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Re: A manufacturer is using glass as the surface  [#permalink]

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New post 24 Dec 2012, 00:25
could you please explain why the power is raised to 10. is it because 10 phone so raise by 10 or any other explanation?
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Re: A manufacturer is using glass as the surface  [#permalink]

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New post 24 Dec 2012, 00:33
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Re: A manufacturer is using glass as the surface  [#permalink]

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New post 18 Oct 2013, 05:36
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probability for one phone passing the test = 0.95
probability for 10 phones passing the test = 0.95 AND 0.95 AND 0.95 ..... = 0.95 * 0.95 * 0.95 .... = 0.95^10
probability for at least one phone not passing the test = 1 - 0.95^10

Answer: C
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Re: A manufacturer is using glass as the surface  [#permalink]

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New post 18 Aug 2016, 02:01
In this case, as written above, it is much easier to calculate the probability that none of the phones will be defect and erase that from 100%.

Probability of passing 1 phone = 0.95.
Probability of passing 10 phones = 0.95*0.95*...*0.95 = 0.95^10
Probability of not passing 10 phones = 1-0.95^10

Answer choice: C
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Re: A manufacturer is using glass as the surface  [#permalink]

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New post 10 Aug 2019, 13:46
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Re: A manufacturer is using glass as the surface   [#permalink] 10 Aug 2019, 13:46
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