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8 June, 19:59

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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  1. 8 June, 22:20
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    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.
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