Question

A population of voters contains 46% Republicans, 45% Democrats and the rest are Independents. Assume 50% of Republicans, 40% of Democrats, and 60% of Independents favor an election issue. A person chosen at random from this population is found to favor the issue in question. Find the conditional probability this person is a democrat. (Round off up to two decimal points.) Group of answer choices 0.18 0.51 0.71 0.39

Answer 1

The probability is 0.18

Explanation:

Here, we are interested in calculating a conditional probability;

Let the event that a voter is a Republican be R , the event that a voter is a Democrat be D and that a voter is an independent is I

Let the event that the election issue is favored be F

We have the following probabilities;

P(R) = 46% = 0.46

P(D) = 45% = 0.45

P(I) = 1-0.45-0.46 = 0.09

The conditional probability we want to calculate is;

P(D | F) which can be read as probability of event D given event F

From the question, we can identify the following conditional probabilities;

P(F|R) = 0.46 * 0.5 = 0.23 (0.5 is gotten from 50% = 50/100)

P(F | D) = 0.45 * 0.4 = 0.18

P( F | I) = 0.09 * 0.6 = 0.054

P(F) = 0.054 + 0.18 + 0.23 = 0.464

Mathematically; From Baye’s theorem

P( D | F) = P ( F / P(F)

P( D | F) = (0.18 * 0.45)/0.464 = 0.1745