the $P(\cos X> \sin X)$

Question

Let the random variable $X$ have uniform distribution on the interval ($\pi/6, \pi/2$), then the $P(\cos X> \sin X)$

Work: $\cos x> \sin x$ on ($\pi/6, \pi/4$) $\subset $ ($\pi/6, \pi/2$) but after that how to find area? Please help.

Answer 1

$X$ is a uniform distribution on $(\pi/6 , \pi/2)$.

Hence the probability is $\frac{\pi/4-\pi/6}{\pi/2-\pi/6}$.

Answer 2

In general, if $X$ is uniformly distributed over an interval $[a,b]$, and $[c,d]\subseteq [a,b]$, you have practically by definition the equality

$$P(x\in [c,d]) = \frac{d-c}{b-a}$$