300 students with 19 out of 50 qualifying means 114 qualify
only 75 are picked via the lottery
which means 39 qualifiers do NOT get picked
39/114 = 13/38 = 0.3421052631578947 (I think)
Maybe this: (as I am not sure what the question is asking)
probability that you are in is 114/300
probability that you LOSE the lottery 39 / 114
multiplied together = 39/300 = 13/100