QUESTION 3.1 In a famous joke, a rather lazy student tosses a coin and decides what to do next. If it turns up heads, play a computer game. If tails, watch a video. If it stands on its edge, do the homework. If it hangs in the air, prepare for an exam. (a) Which events should be assigned probability 0, probability 1, and some probability strictly between 0 and 1? (b) What probability between 0 and 1 would you assign to the event "watch a video," and how does it help you to define "a fair coin"? Response . 5 pointsQUESTION 3.2 A new software package is being tested by specialists. Every day, a number of defects is found and corrected. It is planned to release this software in 30 days. Is it possible to predict how many defects per day specialists will be finding at the time of the release? What data should be collected for this purpose, what is the predictor, and what is the response? Response . 7 pointsQUESTION 3.3 Mr. Cheap plans to open a computer store to trade hardware. He would like to stock an optimal number of different hardware products in order to optimize his monthly profit. Data are available on similar computer stores opened in the area. What kind of data should Mr. Cheap collect in order to predict his monthly profit? What should he use as a predictor and as a response in his analysis? Response . 7 pointsQUESTION 3.4 There is a 2% probability for a hard drive to crash. Therefore, it has two backups, each having a 3% probability to crash, and all three components are independent of each other. The stored information is lost only in an unfortunate situation when all three devices crash. What is the probability that the information is saved? (Hint: Review Example 2.18) Response . 6 pointsQUESTION 3.5 There are 30 computers in a store. Among them, 22 are brand new and 8 are refurbished. Six computers are purchased for a student lab. From the first look, they are indistinguishable, so the six computers are selected at random. Compute the probability that among the chosen computers, two are refurbished. (Hint: Review Example 2.30) Response . 6 pointsQUESTION 3.6 A new computer program consists of two modules. The first module contains an error with probability 0.3. The second module is more complex; it has a probability of 0.4 to contain an error, independently of the first module. An error in the first module alone causes the program to crash with probability 0.5. For the second module, this probability is 0.75. If there are errors in both modules, the program crashes with probability 0.88. Suppose the program crashed. What is the probability of errors in both modules? (Hint: Review Example 2.35) Response . 8 pointsQUESTION 3.7 Of the microprocessors manufactured by a certain process, 20% are defective. Five microprocessors are chosen at random. Assume they function independently. What is the probability that they all work? Response . 5 points