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Math Help - Bag contains 3 red marbles and 2 black marbles

  1. #1
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    Bag contains 3 red marbles and 2 black marbles

    Good afternoon, I'm having some issues with this problem. I would appreciate any help. Thank you!

    1 Bag contains 3 red marbles and 2 black marbles. Two people, B, and C, take turns drawing a marbles from the bag without replacing any of the marbles picked. The 1st person to draw a black marble wins. What is the probability that person B, who always draws first, wins?
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  2. #2
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    Re: Bag contains 3 red marbles and 2 black marbles

    Quote Originally Posted by Schnoodle100 View Post
    1 Bag contains 3 red marbles and 2 black marbles. Two people, B, and C, take turns drawing a marbles from the bag without replacing any of the marbles picked. The 1st person to draw a black marble wins. What is the probability that person B, who always draws first, wins?
    This is a good thought problem.

    In order for $B$ to win it must occur on the first or third drawing. You need to really understand that logic.

    What is the probability that $B$ wins on the first draw?

    What is the probability that $B$ wins on the third draw?
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  3. #3
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    Re: Bag contains 3 red marbles and 2 black marbles

    2/5 on the first draw
    Then something out of 3 for the 3rd draw
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    Re: Bag contains 3 red marbles and 2 black marbles

    Quote Originally Posted by Schnoodle100 View Post
    Good afternoon, I'm having some issues with this problem. I would appreciate any help. Thank you!

    1 Bag contains 3 red marbles and 2 black marbles. Two people, B, and C, take turns drawing a marbles from the bag without replacing any of the marbles picked. The 1st person to draw a black marble wins. What is the probability that person B, who always draws first, wins?
    I don't see any shortcuts to this problem. You're going to have to just develop the entire probability tree for the sequence of outcomes and sum of the probabilities of person B winning.

    here, you can chase down the probability of B winning.

    Bag contains 3 red marbles and 2 black marbles-clipboard02.jpg
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    Re: Bag contains 3 red marbles and 2 black marbles

    Quote Originally Posted by Schnoodle100 View Post
    2/5 on the first draw YES
    Then something out of 3 for the 3rd draw Maybe
    On the third draw there are two conditions to consider:
    did $C$ not win on the second draw and $B$ wins on the third.
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    Re: Bag contains 3 red marbles and 2 black marbles

    So...I'm a little confused as to go about doing this problem
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    Re: Bag contains 3 red marbles and 2 black marbles

    Quote Originally Posted by Schnoodle100 View Post
    So...I'm a little confused as to go about doing this problem
    $\dfrac{2}{5}+\dfrac{3}{5}\dfrac{2}{4}\dfrac{2}{3} $
    Last edited by Plato; May 11th 2014 at 12:27 PM.
    Thanks from Schnoodle100
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    Re: Bag contains 3 red marbles and 2 black marbles

    Alright thank you for all the help!
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