I'm doing this problem:
A student is applying to Harvard and Dartmouth. He estimates that he has a probability of .5 of being accepted at Dartmouth and .3 of being accepted at Harvard. He further estimates the probability that he will be accepted by both is .2. What is the probability that he is accepted by Dartmouth if he is accepted by Harvard? Is the event “accepted at Harvard” independent of the event “accepted at Dartmouth”?
So I begin with the p(D|H)=p(D and H)/p(H) which I find eerily suspicious because is too easy, so is wrong, but why? First the probabilities do not sum to one p(H)+p(D)≠1. So I'm missing something obvious but what??