Quantum physics - homework help needed pleaase!!

[Chelsey2010]

For the infinite square-well potential, find the probability that a particle in its third excited state is in each third of the one-dimensional box:

1. (0< x <L/3)

2 (L/3 <x <2L/3)

3 (2L/3< x< L)

 

I have normalization wave function:

 

sqrt(2/L) sin (npix/L)

 

So for the probability I squared the function and then integrated it from 0 to L/3 (for the first part). I tried this with n=3 and n= 4....but I keep ending up with an incorrect answer. What am I doing wrong?

 

Can someone please help me out with this? I am getting really frustrated.