The Copy Shop has made 20 copies of a document for you. Since the defective rate is 0.1, you think there may be some defective copies in your order, so you leaf through the first ten (which are a randomly chosen subset). If there are 2 defective copies among the 20, what is the probability that you will encounter neither of the defective copies among the 10 you examine

Question

Mathematics

Damaris Beltran

13 October, 06:46

The Copy Shop has made 20 copies of a document for you. Since the defective rate is 0.1, you think there may be some defective copies in your order, so you leaf through the first ten (which are a randomly chosen subset). If there are 2 defective copies among the 20, what is the probability that you will encounter neither of the defective copies among the 10 you examine

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Answers (1)

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Justice Haney · Answer 1

0.2368

Step-by-step explanation:

The probability that you do not encounter a defective copy on the first try is 18/20.

This is because there are 18 non-defective and 2 defective copies you choose from on the first try.

Given that the first one you checked is non defective, the probability of the second being non-defective is now 17/19. This is because the numbers of non-defective and defective are now 17 and 2 respectively.

Similarly the third checked copy being non defective has a 16/18 probability and so forth.

This gives us a pattern as follows:

1. 18/20

2. 17/19

3. 16/18

4. 15/17

...

10. 9/11

Multiplying the probability of the first 10 being non defective we get 0.2368 as the answer.