So I have this problem before me:
Jane is taking two books on her holiday vacation. With probability 0.5, she will like the first book; with probability 0.4 she will like the second book; and with probability 0.3 she will like both books. What is the probability she likes neither?
Now the solution is explained in the book I have, but what I don't understand is how it's possible that Jane will like both books with probability 0.3. Given that she will like the first with 0.5 probability and the second with 0.4, should the probability of Jane liking both be 0.5 * 0.4 = 0.2?