Hi i would like to ask whether my method for decomposition is correct for this P(|X|>|Y|) as i am unable to proceed after this step. Thank you!

3. (10 points) Suppose that X and Y are independent standard normal random variables.c. (4 pts) Find P(X| > [YD).1X1 - 1Y1 20 x 2 > yz ( x + Y ) ( x - Y ) zo Date No. C ) P ( 1 x 1 2 1Y ) ) = P ( 1 x 1 2 2 1 4 1 2 ) = P ( x 2 - 42,0 ) = P((x+Y ) (x- Y) 20) = P(X+Y zo , X- YZO) XTY ~ N ( 0 , # ( 2 ) X-Y~NO, 2 )