You have an error:
The continuous random variable X has probability density function given by:
A is the event X>1/2, B is the event X> 3/4.
Book's answer: 85/152
I have not the faintest idea how to do this, I have tried a few odd approaches but they doesn't match the book's answer: 85/152
I got P(A)=13/32 and P(B)=85/256