Recent ratings for the popular NCIS television show indicate that 7.5% of all television households tune in to the show. The ratings also show that 9.7% of all television households tune in to The Big Bang Theory.

a. Suppose a consultant submits a report saying that it found no one in a sample of 25 homes who claimed to have watched the program NCIS. What is the probability of this happening, assuming that the Nielsen ratings for the show are accurate?

b. Assume the producers for The Big Bang Theory planned to survey 1,000 people on the day following the broadcast of the program. The purpose of the survey was to determine what the reaction would be if one of the leading characters was retired from the show. Based on the ratings, what would be the expected number of people who would end up being included in the analysis, assuming that all 1,000 people could be reached?