Question

In a certain city, 30% of the people are Conservatives, 50% are Liberals, and 20% are Independents. Records show that in a particular election, 65% of the Conservatives voted, 82% of the Liberals voted, and 50% of the Independents voted. If a person in the city is selected at random and it is learned that she did not vote in the last election, what is the probability that she is a liberal

Answer 1

0.31

Explanation:

% conservatives = 30 ; voted = 65%

% Liberals = 50 ; voted = 82%

% Independents = 20 ; voted = 50%

If a person in the city is selected at random and it is learned that she did not vote in the last election, what is the probability that she is a liberal

Number that did not vote :

% conservative × (1 - voted) + % Liberals × (1 - voted) + % conservatives × ( 1- voted)

(30% × 0.35) + (50% × 0.18) + (20% × 0.5)

(0.3 × 0.35) + (0.5 × 0.18) + (0.2 × 0.5)

= 0.105 + 0.09 + 0.1 = 0.295

Hence, probability that a person chosen at random did not vote and she's a liberal :

P = liberal who did not vote / total who did not vote

P = (0.5 × 0.18) / 0.295

P = 0.09 / 0.295

= 0.30508

= 0.31