1. A drawer contains four bags numbered 1 − 4. Bag 1 contains 2 blue and 2 red balls. Bag 2 contains 1 blue and 4 red balls. Bag 3 contains 3 blue balls and Bag 4 contains 7 red balls. You choose a bag at random (with equal probabilities) and then choose a ball at random from that bag. What is the probability for choosing a red ball? What is the probability that the red ball came from bag 2.
2. A multiple choice test consists of 12 questions with 3 possible answers for each question. Student A, who hasn’t studied at all, guesses each answer randomly. Student B, who has studied a lot, answers each problem correctly (and independently) with probability 0.9. (a) What is the probability that the lazy student gets all answers wrong? How about for the hard working student? (b) Assume a student needs at least 10 correct answers to pass the test. For each student separately, compute the probability for passing the test.
3. Several State Lotteries offer, among other games, the so-called Power Ball Game. It works the following way: There are 55 white balls numbered 1 − 55 and 42 red balls numbered 1 − 42 (in separate containers). Every week, 5 white balls and, in addition, one red ball (the Power Ball) are randomly selected. (a) How many possible selections (outcomes) are there for this random experiment? (b) You win the Jackpot if your selection matches all five ”white numbers” and the ”red number”. What is the probability for winning the Jackpot? (c) Compute the probability for matching 4 out of the 5 selected ”white numbers” and the selected red Power Ball number.