Question

find the indicated probability.
in one town, 39% of all voters are democrats. if two voters are randomly selected for a survey, find the probability that they are both democrats. round to the nearest thousandth if necessary.
(1 point)
○ 0.152
○ 0.390
○ 0.372
○ 0.780

Explanation:

Step1: Convert percentage to decimal

The probability of one voter being a Democrat is \(p = 0.39\) (since \(39\%=\frac{39}{100}=0.39\)).

Step2: Use the multiplication rule for independent events

If two events \(A\) and \(B\) are independent, \(P(A\cap B)=P(A)\times P(B)\). Here, the event of the first - voter being a Democrat (\(A\)) and the event of the second - voter being a Democrat (\(B\)) are independent. So \(P(\text{both Democrats})=0.39\times0.39\).

$$0.39\times0.39=(0.4 - 0.01)\times(0.4 - 0.01)=0.4^{2}-2\times0.4\times0.01 + 0.01^{2}=0.16-0.008 + 0.0001=0.1521\approx0.152$$

Answer:

0.152