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Math Help - Conditional Event

  1. #1
    Junior Member
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    Conditional Event

    A box contains 5 green marbles and 4 yellow marbles. Three marbles are drawn at random from the box without replacement. Find the probability that at least 2 yellow marbles are drawn given that at least one of each colour is drawn.

    I've calculated the probability of drawing at least one of each colour is drawn. It's 5/6. The probability of drawing at least 2 yellow marbles is 17/42.

    Now, how do I calculate the probability that at least 2 yellow marbles are drawn given that at least one of each colour is drawn? Many thanks in advance!
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  2. #2
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    Quote Originally Posted by cyt91 View Post
    A box contains 5 green marbles and 4 yellow marbles. Three marbles are drawn at random from the box without replacement. Find the probability that at least 2 yellow marbles are drawn given that at least one of each colour is drawn.

    I've calculated the probability of drawing at least one of each colour is drawn. It's 5/6. The probability of drawing at least 2 yellow marbles is 17/42.

    Now, how do I calculate the probability that at least 2 yellow marbles are drawn given that at least one of each colour is drawn? Many thanks in advance!
    hi

    do you recognise this ? P(A|B)=P(A n B)/P(B)

    so the condition here is at least one of each colour is drawn , call it B

    and the event that at least 2 yellow marbles are drawn , A

    P(A n B)=(5C1 x 4C2)/9C3=5/14

    so P(A|B)=(5/14)/(5/6)=3/7
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  3. #3
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    Thanks. Found it.
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