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Math Help - Continuous random variable P(B|A) when A=X>1/2, B=X>3/4

  1. #1
    Member ssadi's Avatar
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    Continuous random variable P(B|A) when A=X>1/2, B=X>3/4

    The continuous random variable X has probability density function given by:

    f(x)=\frac{3}{4} (1+x^2), for 0\leq x \leq 1, and 0, otherwise
    A is the event X>1/2, B is the event X> 3/4.
    Find P(B|A).
    Book's answer: 85/152

    I have not the faintest idea how to do this, I have tried a few odd approaches but they doesn't match the book's answer: 85/152
    I got P(A)=13/32 and P(B)=85/256
    :help:
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    P\left( {B|A} \right) = \frac{{P(B \cap A)}}{{P(A)}} = \frac{{P(B)}}{{P(A)}}

    You have an error: P(A)=\frac{{\color{red}19}}{32}
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