A political scientist askeda group of people how they felt a

A political scientist askeda group of people how they felt about 2 political policy statements. Each person was to respond A(agree), N(neurtal) or D(disagree) to each of the 2 statements.

A. Describe the sample space to the 2 statements

AA, AN, ...........

B. assuming each response pair in the sample space is equally likely what is the probability that:

1. the person agrees with at least one of the 2 statements P(at least one)=

2. the person agrees with exactly one on the 2 statments P(exactly one)=

3. the person agrees with both statements P(both)=

Solution

A) Sample space = {AA, AN, AD,NA, ND, NN, DA, DN, DD}

As each is equally likely each has prob 1/9

1) Prob agrees atleast one of two statements = Full sample space -{ND, NN, DN, DD} = 5/9

2) Prob the person agrees with exactly one of the two statement

= {AN, AD,NA, DA} = 4/9

3) Prob for agreeing with both = P(AA) = 1/9