1. If a student randomly guesses at five multiple-choice questions, find the probability that the student gets exactly three correct. Each question has five possible choices.
2. Say 40% of the class is female. What is the probability that 6 of the first 10 students walking in will be female?
3. Telephone manufacturers now offer 1000 different choices for a telephone (as combinations of color, type, options, portability, etc.). A company is opening a large regional office, and each of its 200 managers is allowed to order his or her own choice of a telephone. Assuming independence of choices and that each of the 1000 choices is equally likely, what is the probability that a particular choice will be made by none, one, two, or three of the managers?
4. The mean number of power outages in the city is four (4) per year. Find the probability that in a given year, there are exactly three (3) outages.