Calculating mutual events with continuous distribution Suppose $\ X \sim U(-4,7) $
Compute: $\ P\{X^2 - 16 > 0 \ | \ X > 0 \} $
My attempt:
$$\ P\{ X^2 - 16 > 0 | X>0 \} = P \{ X > 4 | X > 0 \} = \frac{P\{X>4\}}{P\{X>0\} } $$
I'm just not sure I understand what how to calculate the probability of $\ P\{ X > a \}  \cap P\{X > b\} $ with continues variables. Is it equal to $\ P\{X > a \} \cdot P\{X >b \} $
When I draw a uniform distribution it's seems like it is $\ P\{ X > a | X >b \} = \frac{P\{X>a\}}{P\{X>b\}} $ where $\ a > b $ but I'm not sure.

Well what is the intersection of the sets? What does it mean if $\omega$ is fulfilling $X(\omega) > a$ and $X(\omega) > b$?
