A library has classified its books into fiction and nonfiction. Furthermore, all books can also be described as hardback and paperback. As an experiment, we shall pick a book at random and record whether it is fiction or nonfiction and whether it is paperback or hardback.
(a) Describe the sample space, i.e., list all outcomes.
(b) Describe the event space, i.e., list all events.
(c) Define a probability measure such that the probability of picking a nonfiction paperback is 0.15, the probability of picking a nonfiction book is 0.30, and the probability of picking a fiction hardback is 0.65. (d) Using the probabilities from part (c), find the probability of picking a fiction book given that the book chosen is known to be a paperback.