Question

In one​ town, 50​% 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.

Answer 1

Given :- 50​% of all voters are democrats.

Probability that randomly selected voter will be a democrat = 0.50.

Independent event Property :- If two events A and B are independent on each other then P(A and B) = P(A) * P(B).

In this question, Vote of one person is independent on another person. Every individual's vote preference is independent.

The probability that they are both democrats

= P( first is democrat AND second is also a democrat)

=P(first is democrat) * P(second is also a democrat)

= 0.50 * 0.50 (Using above property of independent events)

= 0.25

Answer :- If two voters are randomly selected for a​ survey, Then the probability that they are both democrats is 0.25.