Because Ψ(x,0) is real we just square it.
2. Write Ψ(x,π/3), the wavefunction at t=π/3.
3.Write |Ψ(x,π/3)|2, which determines position probabilities at t=π/3. Simplify your answer.
You can find the modulus squared by multiplying an expression by its own complex conjugate, which you can generally get by replacing i with -i.
When you combine the exponential terms using rules of exponentials (eaeb=ea+b) you get e0, which is just 1. So:
4. How did the position probabilities change between these two times?
The position probabilities did not change.