Question

7. A survey of 1000 registered voters found that 325 had voted in the most recent local election, 415 had voted in the most recent national election, and 245 had voted in both. If a surveyed person is randomly selected, what is the percent probability that he or she voted in the most recent local or national election? Express your answer to the nearest tenth of a percent, decimal and fraction.

Answer 1

To find the percent probability that a randomly selected surveyed person voted in the most recent local or national election, we need to calculate the union of the probabilities.

Given:
- Number of surveyed voters who voted in the most recent local election (A) = 325
- Number of surveyed voters who voted in the most recent national election (B) = 415
- Number of surveyed voters who voted in both elections (A ∩ B) = 245

To find the percent probability, we'll calculate the total number of surveyed voters who voted in either election (A ∪ B) and divide it by the total number of surveyed voters (N = 1000).

Total number of surveyed voters who voted in either election (A ∪ B) = (A + B) - (A ∩ B)
= (325 + 415) - 245
= 495

Percent probability = (A ∪ B) / N * 100
= 495 / 1000 * 100
= 49.5%

Therefore, the percent probability that a randomly selected surveyed person voted in the most recent local or national election is 49.5%, which can be expressed as 0.495 (decimal) or 495/1000 (fraction).