1.) a survey questioned 1,000 high school students. the survey revealed that 48% are honor roll students. of those who are honor roll students, 45% play sports in school and 22% of those that are not honor roll students, don’t play sports. what is the probability that a high school student selected at random plays sports in school?

2.) one of two small restaurants is chosen at random with equally likely probability, and then an employee is chosen at random from the chosen restaurant. Restaurant #1 has 10 full-timers and 6 part-timers. Restaurant #2 has 7 full-timers and 9 part-timers. What is the probability that Restaurant #1 was chosen at random, given that a full-time employee was chosen?

3.) The expected lifetime of a television is 18 years with a standard deviation of 4. Use Chebychev’s inequality to estimate the probability that television will last between 9 and 27 years.

4.) Consider the following binomial experiment. The probability that a child in a certain age group will get the chicken pox is 0.78. Find the probability that among 7 children in this certain age group all of them will get the chicken pox.

5.) Consider the following binomial experiment. A company owns 6 machines. The probability that on a given day any one machine will break down is 0.59. What is the probability that at least 4 machines will break down on a given day.