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Math Help - Marbles in a jar (probability)

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    Marbles in a jar (probability)

    A jar contains a marble, it may is black or white with the same probability.
    We put a white marble in the jar and then we draw a marble. Suppose that the marble we draw is white. What is the probability the first draw to be black?

    Facts:
    W: the first marble is white, B: the first marble is black.
    DW: we draw a white marble, DB: we draw a black marble.


    I think the answer is 1/2 but how can i proove it ? Can anybody help me ?
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    Quote Originally Posted by Anglela View Post
    A jar contains a marble, it may is black or white with the same probability.
    We put a white marble in the jar and then we draw a marble. Suppose that the marble we draw is white. What is the probability the first draw to be black?

    Facts:
    W: the first marble is white, B: the first marble is black.
    DW: we draw a white marble, DB: we draw a black marble.


    I think the answer is 1/2 but how can i proove it ? Can anybody help me ?
    Draw a tree diagram. It will make the following answer (based on conditional probability) easier to understand: \displaystyle \frac{\frac{1}{4}}{\frac{1}{4} + \frac{1}{2}} = \frac{1}{3}.
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