Information from a poll of registered voters in Cedar Rapids, Iowa, to assess voter support for a new school tax was the basis for the following statements (Cedar Rapids Gazette, August 28, 1999):

The poll showed 51 percent of the respondents in the Cedar Rapids school district are in favor of the tax. The approval rating rises to 56 percent for those with children in public schools. It falls to 45 percent for those with no children in public schools. The older the respondent, the less favorable the view of the proposed tax: 36 percent of those over age 56 said they would vote for the tax compared with 72 percent 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:

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

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

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i. P(F) ii. P(F|C) iii. P(FCC) iv. P(FO) v. P(FY)