probability question (data)

Question

5 students were surveyed. 15 take both biology and physics. 42 take biology and 32 take physics. Use Venn diagram to organize this data then calculate the probability that a student selected at random from this group does not take physics.

Answer 1

So, I think there is something wrong with this question. I don't think it is solvable. The size of the sum of two sets is exactly the size of one plus the size of the other, minus their overlap. That means that the amount of students that take either biology or physics must be 42+32-15. Size A + Size B - Size A&B. And so that number, 42+32-15 is equal to 59. But that doesn't make sense, since our sample size is said to be 50. We can't have the classes of 59 kids if we only surveyed 50. Unless it's just late and I'm missing something very obvious (wouldn't be the first time), I think this question is broken.