Question

A population of voters contains 40% republicans and 60% democrats. it is reported that30% of the republicans and 70% of the democrats favor an election issue. a person chosenat random from this population is found to favor the issue in question. find the conditionalprobability that this person is a democrat

Answer 1

To get the probability of selecting a person who is a democrat and is favour to the issue, let us first calculate for the portions in each party who is favour on the issue.

 

p (rep & favour) = 0.4 * 0.3 = 0.12

 

p (dem & favour) = 0.6 * 0.7 = 0.42

 

Therefore the total portions who are favour is:

p (favour) = 0.12 + 0.42 = 0.54

 

Hence the probability is:

P (dem & favour) = 0.42 / 0.54 = 0.7778 = 0.78

 

Therefore there is about 78% probability that the person selected who is favour to the issue is a democrat.