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Math Help - Prob. Distribution problem. Help Please.

  1. #1
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    Prob. Distribution/Random Variable problem

    Roll a dice 4 times
    X = smallest face observed
    Given P(X=6) = 1/1296

    Find:
    P(X=1)
    P(X=2)
    P(X=3)
    P(X=4)
    P(X=5)

    I got 216/1296, 125/1296, 64/1296, 27/1296, and 8/1296 for P(X=1) through P(X=5) respectively. I think I did something wrong as the numerators don't add up to 1296 like I thought they would.

    Help is appreciated.

    This is a probability distribution function by the way.
    Last edited by Iceflash234; October 21st 2010 at 03:14 AM.
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  2. #2
    MHF Contributor matheagle's Avatar
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    show your work
    For the event X=1, that means you had at least one 1.

    so P(X=1)=1-P({\rm no}\quad  1's)=1-(5/6)^4
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  3. #3
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    Quote Originally Posted by matheagle View Post
    show your work
    For the event X=1, that means you had at least one 1.

    so P(X=1)=1-P({\rm no}\quad  1's)=1-(5/6)^4
    Here's my for the solutions in the first post:

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  4. #4
    MHF Contributor matheagle's Avatar
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    what about switching the order?
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  5. #5
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    Quote Originally Posted by matheagle View Post
    what about switching the order?
    What order? I'm so confused on how to do this. I know how to get P(X=1) but how do I get P(X=2) and so on?
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  6. #6
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    I know I must be missing something because I didn't think this was supposed to be this hard of a problem.
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  7. #7
    MHF Contributor matheagle's Avatar
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    P(X=2)=4(1/6)(5/6)^3
    You keep assuming that the first toss is a two, it can be a 3,3,3,2.
    So there are 4 places to put down a 2.
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