Dr. Patterson is a veterinarian who sees only dogs and cats. In each appointment, he may or may not give the animal a vaccine. The two-way frequency table summarizes Dr. Patterson's 80 appointments last week. Vaccine No vaccine Dog Cat 27 12 33 8 Let cat be the event that a randomly chosen appointment (from the table) involved a cat. Let vaccine be the event that a randomly chosen appointment (from the table) included a vaccine. Find the following probabilities. Write your answers as decimals. (a) P(cat) = = 0 (b) P(vaccine and cat) = (c) P(vaccine | cat) =