Random variable conditioning

[sneaky666]

Homework Statement

Let X and Y be jointly absolutely continuous Random Variables. Suppose X~Exponential(2) and that P(Y>5|X=x)=e^-3x. Compute p(Y>5).

Homework Equations

X~Exponential(2) means that its a exponential distribution integrated from -inf to inf, then sub lambda as 2.

The Attempt at a Solution

the answer is 2/5 which is given but i don't get that... here is my prof's solution somehow he got 2/5
http://i.imgur.com/PCgDI.jpg

I don't understand how to get it, i end up getting infinity in the last step

 

[sneaky666]

nvm i figured it out