In a task i get the following density function: $f_{X,Y}(x,y)=6e^{-3x}e^{-2y}$ if $\ 0\ < x \ < \infty$ and $\ 0 < y < \infty$.
I'm asked to calculate: $P(X+1< Y)$ and this was my first try:
$$\int_0^\infty \int_0^{y-1}6e^{-3x}e^{-2y} dxdy =1-\frac{2e^3}{5}$$ which is wrong.
Second try: $$\int_0^\infty \int_{x+1}^\infty6e^{-3x}e^{-2y} dydx=\frac{3e^2}{5}$$ which is correct.
Every time I get a task like this, it is done wrong. Can explain to me, how I should choose the correct interval, please?