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Math Help - basic conditinal prob.

  1. #1
    Senior Member sfspitfire23's Avatar
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    basic conditinal prob.

    You flip a coin and a die once


    Let A = head and let B = get a six


    You run the experiment and you are told that at least one event occurred.


    What is the probability that both A and B occurred?

    at least = 7/12

    But dont know how to calculate P(AB | A u B)
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  2. #2
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    Re: basic conditinal prob.

    Sfspitfire

    The events A and B are independent therefore P(A and B) = P(A)P(B) = (1/2)(1/6) =1/12

    P(AUB) = P(A)+P(B)-P(A and B)
    The conditional robability P(X/Y) =(P(X and y))/P(Y) JUST APPLY THE FORMULA..ITS EASY
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  3. #3
    Senior Member sfspitfire23's Avatar
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    Re: basic conditinal prob.

    No, you're incorrect. The answer is 1/7. There's no way that they're independent.
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    Re: basic conditinal prob.

    Quote Originally Posted by sfspitfire23 View Post
    No, you're incorrect. The answer is 1/7. There's no way that they're independent.
    Apply Bayes Rule: \frac{\frac{1}{12}}{\frac{1}{12}+\frac{5}{12}+ \frac{1}{12}}
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    Re: basic conditinal prob.

    Definition of independent event:

    Independent events are events which have no effect on one another.
    In your case how the result of the coin will have any effect on the result of the dice?
    This is wrong ....

    I suggest you to consult a good book on probabilities ( STATISTICS1 STEVE DOBBS & JANE MILLER PAGE 76 EXAMPLE 4.5.1 )

    minoas
    Last edited by MINOANMAN; March 7th 2013 at 07:59 AM.
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  6. #6
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    Re: basic conditinal prob.

    The coin can be T or H, the die can be 1, 2, 3, 4, 5 or 6, each of those being "equally likely".

    So, when a coin is flipped and a die is rolled, the "equally likely" events are
    T, 1
    T, 2
    T, 3
    T, 4
    T, 5
    T, 6
    H, 1
    H, 2
    H, 3
    H, 4
    H, 5
    H, 6
    You are told that "at least one" of "Heads" and "6" occured so that reduces to
    H, 1
    H, 2
    H, 3
    H, 4
    H, 5
    H, 6
    T, 6
    a total of 7 equally likely events. "Both A and B", that is, a Head and a 6, is one of those 7 events: probability of "head and 6" given that at least one of "head" and "6" occured is 1/7.
    Last edited by HallsofIvy; March 7th 2013 at 08:30 AM.
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