Basic brownian motion computation

Question

Let $B_t$ denote a standard 1-d Brownian Motion. Find $P(B_2 \gt 2)$.

My sol.

$B_2 ~ N(0,2)$ so $P(B_2 \gt 2)=1-P(B_2\le 2)=1-\frac{\int_0^2e^{-\frac{x^2}{4}}}{\sqrt{4\pi}}$, but where do i go from here,

Any help would be appreciated, thanks

Answer 1

The integral should start at $-\infty$. You basically got it. If you want a number your have to numerically evaluate the integral.