1. A "true-false" exam has 10 questions. Assuming that the questions are independent and that a student is guessing, find the probability that they get 100%?
2. A TV set contains five circuit boards of type A, five of type B, and three of type C. The probability of failing in its first 5000 hours of use is .01 for a type A circuit board, .02 for a type B circuit board, and .025 for a type C circuit board. Assuming that the failures of the various circuit boards are independent of one another, compute the probability that no circuit board fails in the first 5000 hours of use.
3. In November 2015, Intel announced the release of a business desktop computer with 72 processor cores. Suppose the probability that a given processor core will crash in 120 hours of use is .003, and that the failures of the various processor cores are independent of one another. What is the probability that no processor core will crash during the first 120 hours of use?
4. Suppose that in Sleepy Valley, 70% of those over 50 years old own smart-phones. Find the probability that among four randomly chosen people in that age group, none owns a smart-phone?