The probability that a student who does not have a dog has a cat can be found by taking the number of students who have a cat but do not have a dog (which is 12) and dividing by the total number of students who do not have a dog (which is 3+5 = 8). Therefore, the probability is:
12/8 = 3/2 or 1.5
However, probabilities cannot be greater than 1, so the answer is not valid. This might be because of some mistake in the data or in the calculation. It could be that there is some overlap between the two categories (some students could have both a cat and a dog), or that the data is incomplete. In any case, without more information, we cannot give a valid probability for this question.