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Thread: Conditional probability help

  1. #1
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    Conditional probability help

    Hello! I am stuck on one part of this problem:

    Suppose that X and Y have the joint pdf f_x,y(x,y)=(xy^2)/39 for the points (1,2), (1,3), (2,2), and (2,3). Find the conditional probability that X is 1 given that Y is 2.

    I understand that conditional probabilities can be solved with f_x,y(x,y)/f_x(x) but I think my calculations are off. I've tried many times and the answers I've gotten were .1875 and .15 but those are not right.
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  2. #2
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    Re: Conditional probability help

    $P[X=1|Y=2]=\dfrac{P[X=1 \wedge Y=2]}{P[Y=2]} = \dfrac{\frac{4}{39}}{\frac {4}{39} + \frac{8}{39}} = \dfrac 1 3$
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