An opinion poll is conducted among a states electorate to de

An opinion poll is conducted among a state\'s electorate to determine the relationship between their income levels and their stands on a proposition aimed at reducing state income taxes. Voters are classified as belonging to either the low-, middle-, or upper-income group. They are asked whether they favor, oppose, or are undecided about the proposition. Let the letters L, M, and U represent the low-, middle-, and upper-income groups, respectively, and let the letters f, o, and u represent their responses-favor, oppose, and undecided, respectively. (Enter your answers using letter combinations separated by commas. Example: Lf, Uu, ...) (a) Describe a sample space S corresponding to this poll. (b) Describe the event E_1 that a respondent favors the proposition. (c) Describe the event E2 that a respondent opposes the proposition and does not belong to the low-income group. (d) Describe the event E3 that a respondent does not favor the proposition and does not belong to the upper-income group.

Solution

a) Sample space = Each voter can belong to either of low, middle or upper class. He can also vote either in favor or oppose the proposition. This means the sample space which consists of all possible combinations would be:

(L,f), (L, o), (L, u), (M, f) (M,o), (M, u), (U,f), (U, o), (U,u)

b) The event that favors the proposition can have the following outcomes:

{ (L,f), (M,f), (U,f) }

c) The event that a respondent opposes the proposition and does not belong to the low-income group can have the following outcomes : { (U,o), (M,o) }

d) The event that a respondent does not favour the proposition and does not belong in the upper-income group can have the following outcomes: { (M,u), (M,o), (L,o), (L,u) }