Question

2. In a given country, records show that of the registered voters, 45% are Democrats, 35% are Republicans, and 20% are independents. In an election, 70% of the Democrats, 40% of the Republicans, and 80% of the independents voted in favor of a parks and recreation bond proposal. If a registered voter chosen at random is found to have voted in favor of the bond, what is the probability that the voter is a Republican? An independent? A Democrat? (Please show all work for full credit and have a legend for symbols).

Answer 1

P(R) = 0.14

P(I) = 0.16

P(D) = 0.315

Explanation:

Let Democrat = D

Republican = R

Independent = I

If 45% are Democrats, 35% are Republicans, and 20% are independents, then

Total registered voters = 100

In an election, 70% of the Democrats, 40% of the Republicans, and 80% of the independents voted in favor of a parks and recreation bond proposal. That is,

D = 0.7 × 45 = 31.5

R = 0.4 × 35 = 14

I = 0.8 × 20 = 16

If a registered voter chosen at random is found to have voted in favor of the bond, what is the probability that the voter is

a Republican:

P(R) = 14 /100 = 0.14

an Independent

P(I) = 16/100 = 0.16

a Democrat

P(D) = 31.5/100 = 0.315