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

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• January 24th 2009, 10:08 AM
ssadi
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:
• January 24th 2009, 10:23 AM
Plato
$P\left( {B|A} \right) = \frac{{P(B \cap A)}}{{P(A)}} = \frac{{P(B)}}{{P(A)}}$

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