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Math Help - probability problem

  1. #1
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    probability problem

    a woman has 10 keys out of which only one opens a lock.she tries the keys one after the another (keeping aside the failed ones) till she succeeds in opening the lock. what is the chance that it is the seventh key that works
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    MHF Contributor Unknown008's Avatar
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    Each time she uses a key, the probability that she chooses the correct one increases.

    Let X be the key number which fits.

    P(X = 7) = (\frac{9}{10})(\frac89)(\frac78)(\frac67)(\frac56)  (\frac45)(\frac14)

    In brief, you'll see that P(X = n) = \frac{1}{10}
    Last edited by Unknown008; October 3rd 2010 at 09:21 AM.
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  3. #3
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    Quote Originally Posted by Unknown008 View Post
    Each time she uses a key, the probability that she chooses the correct one increases.

    Let X be the key number which fits.

    P(X = 7) = (\frac{9}{10})(\frac89)(\frac78)(\frac67)(\frac56)  (\frac45)(\frac14)

    In brief, you'll see that P(X = n) = \frac{1}{10}
    thanks
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