Question

In one town , 54% of all voters are Democrats. If two voters are randomly selected for a survey, find the probability that they are both democrats. Round to three decimal places

Answer 1

Two voters are a very small percentage of the town's population so we can treat each of the two selections as independent events.

Event A = pick first democrat = 54% = 54/100 = 0.54

Event B = pick second democrat = 0.54

Since A and B are independent we have:

$P(A\text{ and B)=}P(A)\times P(B)$

Substitute the values:

$P(A\text{ and B)=0.54}\times0.54=0.292$

Answer: 0.292