A particle is in the ground state of an infinite square well with walls at x=0 and x=a. Suddenly, a new wall is inserted at x=a/2, splitting the well into two halves. What is the probability of finding the particle in the ground state of the left half? [You may want to use the fact that ∫0a/2sin(πx/a)sin(2πx/a)dx=0.]