An opinion poll is conducted among a state\'s electorate to determine the relati

Question

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.
S =

(b) Describe the event E1 that a respondent favors the proposition.
E1 =

(c) Describe the event E2 that a respondent opposes the proposition and does not belong to the low-income group.
E2 =

(d) Describe the event E3 that a respondent does not favor the proposition and does not belong to the upper-income group.
E3 =

Explanation / Answer

Solution:

a) Smple space consists of 3 income brackets * 2 decisions = 6 outcomes

S = {(L,f), (L,o), (M,f), (M,o), (U,f), (U,o)}

b) All the items in the sample space that include the "f" designation

E1 = {(L, f), (M, f), (U, f)}

c) All the terms with an "o" designation EXCEPT the Low income one

E2 = {(M, o), (U, o)}

d) All the terms with an "o" designation PLUS the M income bracket in favor of the proposal

E3 = {(L, o), (M, o), (U, o), (M, f)}

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