The following table gives the percent of eligible voters grouped according to profession who responded with "Voted" in the 2000 presidential election. The table also gives the percent of people in a survey categorized by their profession. If an eligible voter who participated in the survey and voted in the election is selected at random, what is the probability that this person is a farmer?
A) 0.9213
B) 0.6910
C) 0.1800
D) 0.0787
E) 0.0208

Question

The following table gives the percent of eligible voters grouped according to profession who responded with "Voted" in the 2000 presidential election. The table also gives the percent of people in a survey categorized by their profession.  If an eligible voter who participated in the survey and voted in the election is selected at random, what is the probability that this person is a farmer?
A) 0.9213 
B) 0.6910 
C) 0.1800 
D) 0.0787 
E) 0.0208

Quizplus · Accepted Answer

To find the probability that a selected person is a farmer and voted in the election, we need to use conditional probability.

Let F denote the event that the selected person is a farmer and V denote the event that the selected person voted in the election.

We want to find P(F|V), the probability that the selected person is a farmer given that they voted in the election.

Using Bayes' theorem, we have:

P(F|V) = P(V|F) * P(F) / P(V)

P(V|F) is the percent of farmers who responded with "Voted" in the election, which is 42%. 
P(F) is the percent of people in the survey who are farmers, which is 18%. 
P(V) is the overall percent of eligible voters who voted in the election, which is the sum of the products of the percent of people in the survey and the percent of those who voted in the election for each profession:

P(V) = (24% * 91.3%) + (18% * 42%) + (14% * 63.9%) + (24% * 61.8%) + (20% * 50.1%) = 62.83%

Plugging in the values, we get:

P(F|V) = (0.42 * 0.18) / 0.6283 = 0.0787

Therefore, the probability that the selected person is a farmer given that they voted in the election is 0.0787, which is approximately 7.87%, or choice D.

The Following Table Gives the Percent of Eligible Voters Grouped