Anne and Jane have shoes spread throughout the dorm room. Anne has 15 pairs of shoes; twenty percent of her shoe collection consists of sandals. Jane has 40 pairs of shoes; ten percent of her shoe collection consists of sandals.
a. A shoe is picked at random from the dorm room belonging to Anne and Jane; what is the probability that it is a sandal?
b. If a randomly chosen shoe is chosen from the room (with all shoes equally likely to be chosen), what is the probability that it belongs to Anne?
c. If a randomly chosen shoe is chosen from the room (with all shoes equally likely to be chosen), and upon examination this shoe is seen to be a sandal, what is the probability that it belongs to Anne?