Question

In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 75 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?(A) 50%(B) 53%(C) 54%(D) 55%(E) 57%

Answer 1

Answer: (B) 53%

Explanation:

Given : The probability that registered voters are Democrats P(D)= 0.60

The probability that of registered voters are Republicans P(R)= 100%-60%=40% =0.4

The probability that the registered voters who are Democrats are expected to vote for Candidate A : P(A|D)=0.75

The probability that the registered voters who are Republicans are expected to vote for Candidate P(A|R) = 0.20

Then by using Law of total probability , the probability of the registered voters are expected to vote for Candidate A :-

`P(A)= P(D)\cdotP(A|D)+P(R)\cdotP(A|R)\\\\=0.60*0.75+0.40*0.20\\\\=0.45+0.8\\=0.53=53\%`

Hence, the percent of the registered voters are expected to vote for Candidate A=53%

Hence, the correct option is (B).