The data file Colleges contains data on more than 1,300 colleges and universities in the United States. Suppose a company is planning to award a significant grant to a randomly selected college or university. Using the relative frequency method for assessing probabilities and the rules of probability, respond to the following questions. (If data are missing for a needed variable, reduce the number of colleges in the study appropriately.)
a. What is the probability that the grant will go to a private college or university?
b. What is the probability that the grant will go to a college or university that has a student/faculty ratio over 20?
c. What is the probability that the grant will go to a college or university that is both private and has a student/faculty ratio over 20?
d. If the company decides to split the grant into two grants, what is the probability that both grants will go to California colleges and universities? What might you conclude if this did happen?