Question

A total of 46 percent of the voters in a certain city classify themselves as Independents, whereas 30 percent classify themselves as Liberals and 24 percent say that they are Conservatives. In a recent local election, 35 percent of the Independents, 62 percent of the Liberals and 58 percent of the Conservatives voted. A voter is chosen at random. Given that this person voted in the local election, what is the probability that he or she is

(a) an Independent?
(b) a Liberal?
(c) a Conservative?
(d) What fraction of voters participated in the local election?

Answer 1

a) 0.161

b) 0.186

c) 0.1392

d) 2431/5000

Explanation:

Voters

Independents - 46% =

Liberals - 30% =

Conservatives - 24% =

Elections:

Independents - 35% = 0.35

Liberals - 62% = 0.62

Conservatives - 58% = 0.58

what is the probability that he or she is

(a) an Independent?

0.46*0.35 = 0.161

(b) a Liberal?

0.3*0.62 = 0.186

c) a Conservative?

0.24*0.58 = 0.1392

(d) What fraction of voters participated in the local election?

0.161 + 0.186 + 0.1392 = 0.4862 = 4862/10000 = 2431/5000