Another Quick Couple of Infinite Well Questions

[G01]

Homework Statement

Problem 1. If I had a wavefunction: \Psi(x,0) = A(\psi_1(x) + \psi_2(x))

What is the probability of getting E1 or E2 as your energy?

Problem 2 You have a wavefunction:

\Psi(x,0) = Ax; 0<= x <= a/2 ; A(a-x); a/2<= x <= a
What is the probability that an energy measurement would yield E1.

Homework Equations

Given Up above

The Attempt at a Solution

For problem 1, i feel the probabilities should be 1/2 for each of them, but this seems too easy. I also normalized and found Psi(x,t), A = 1/sqrt(2)

For problem 2 I'm completely lost
There are an infinite amount of energy levels so shouldn't the probability be 0, but then this doesn't make any sense. I feel I'm missing something. Are the probabilities not that easy?

 

[G01]

wait, just remembered...i got to find c_n^2...