One version of DeMorgan's Law states:
/'(neither A nor B) = P (A and B) = 1 - P(A or B)
A survey was conducted to gauge support for a dedicated road tax. The respondents for a particular city were divided into those who live in the inner city and those who live in the suburbs. A third category was created for those living outside the city. The percentage of respondents living in the inner city is 12.6% and the percentage living in the suburbs is 79.3%, with the remainder living outside the city forming the remaining percentage of respondents. Responses were classified as support the tax, oppose the tax, and undecided. The percentage overall who support the tax is 45.2%, while the percentage who oppose the tax is 32.3%. The percentage of respondents who live in the inner city and support the tax is 8.5%. The percentage of respondents who live in the inner city and oppose the tax is 1.8%. The percentage of respondents who live in the suburbs and oppose the tax is 27.6%. The percentage of respondents who live outside the city and are undecided is 4.3%.
a. Create a contingency table based on these probabilities.
b. Using the addition rule, compute the probability that a respondent lives in the city or does not support the tax.
c. Using DeMorgan's Law, compute the probability from part (b).