Answer Happy

Exercise 2.5. Jane takes two books on a vacation. With probability 0.6 she likes the first book, with probability 0.5 she likes the second book, and with probability 0.4 she likes both books. What is the probability that she likes neither book? Hint: You have to find P((BUB)), where B, k = 1,2, is the event that Jane likes the i-th book. 3 Exercise 2.6. Alice and Bob take turns in throwing a fair die, in this order. Then Alice starts again, and so on. The first one to get a '6' wins. What is the probability that Alice wins? Exercise 2.7. Use the inclusion-exclusion formula to compute the probabil- ity that a randomly chosen number between 000 and 999 contains at least one 1. Exercise 2.8. Solve the previous problem using the probability of the com- plementary event that the number does not contain a 1.