A manufacturer is using glass as the surface

Question

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

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

Bunuel · Accepted Answer

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.

fozzzy · Answer

could you please explain why the power is raised to 10. is it because 10 phone so raise by 10 or any other explanation?

Bunuel · Answer

The probability that a phone will pass the test is 0.95, thus the probability that all 10 phones will pass the test is P(all 10 phones pass test)=0.95^10.

Spunkerspawn · Answer

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

MarkusKarl · Answer

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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A manufacturer is using glass as the surface

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A manufacturer is using glass as the surface

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