I believe this is correct, however my issue is that the question specifically asks for the probability of the second state, which would be the second coefficient squared. Perhaps I have it wrong, but if you omit the even coefficients in that graph I think the same graph should be produced. Thank...
Firstly I have found the eigenstates for both the original well and the new well as the following
$$\psi_{n,\frac{L}{2}} = \begin{cases} \sqrt{\frac{2}{L}} \cos{\frac{n \pi x}{L}} \; \; \; \; \; n \text{ odd} \\ \sqrt{\frac{2}{L}} \sin{\frac{n \pi x}{L}} \; \; \; \; \; n \text{ even}...