Information from a poll of registered voters in a city to assess voter support for a new school tax was the basis for the following statements. The poll showed 53% of the respondents in this city's school district are in favor of the tax. The approval rating rises to 59% for those with children in public schools. It falls to 45% for those with no children in public schools. The older the respondent, the less favorable the view of the proposed tax: 36% of those over age 56 said they would vote for the tax compared with 72% of 18- to 25-year-olds.

Suppose that a registered voter from Cedar Rapids is selected at random, and define the following events: F =event that the selected individual favors the school tax, C event that the selected individual has children in the public schools, O event that the selected individual is over 56 years old, and Y event that the selected individual is 18—25 years old.

a. Use the given information to estimate the values of the following probabilities:
i. P(F)
ii. P(F|C)
iii. P(F|C^C)
iv. P(F|O)
v. P(F|Y)

b. Are F and C independent? Justify your answer.
c. Are F and O independent? Justify your answer.