The report “Twitter in Higher Education: Usage Habits and Trends of Today’s College Faculty” (Magna Publications, September 2009) describes a survey of nearly 2,000 college faculty. The report indicates the following: 30.7% reported that they use Twitter, and 69.3% said that they do not use Twitter. Of those who use Twitter, 39.9% said they sometimes use Twitter to communicate with students. Of those who use Twitter, 27.5% said that they sometimes use Twitter as a learning tool in the classroom. Consider the chance experiment that selects one of the study participants at random.
a. Two of the percentages given in the problem specify unconditional probabilities, and the other two percentages specify conditional probabilities. Which are conditional probabilities, and how can you tell?
b. Suppose the following events are defined: T = event that selected faculty member uses Twitter C = event that selected faculty member sometimes uses Twitter to communicate with students L = event that selected faculty member sometimes uses Twitter as a learning tool in the classroom Use the given information to determine the following probabilities
i. P(T)
ii. P(T C)
iii. P(C| T)
iv. P(L| T)
5.80 (M9) USA Today (June 6, 2000) gave information on seat belt usage by gender. The proportions in the following table are based on a survey of a large number of adult men and women in the United States:
c. Construct a “hypothetical 1000” table using the given probabilities and use it to compute P(C), the probability that the selected study participant sometimes uses Twitter to communicate with students.
d. Construct a “hypothetical 1000” table using the given probabilities and use it to compute the probability that the selected study participant sometimes uses Twitter as a learning tool in the classroom.