At Andrew Jackson High School, students are only allowed to enroll in AP U.S. History if they have already taken AP World History or AP European History. Out of 825 incoming seniors:

- 175 took AP World History
- 36 took AP European History
- 33 took both AP World History and AP European History

Given this information, determine the probability that a randomly selected incoming senior is allowed to enroll in AP U.S. History.

To determine the probability, we add the number of students who took AP World History and AP European History and subtract the number of students who took both. Out of 825 incoming seniors, 178 are allowed to enroll in AP U.S. History. The probability is approximately 0.216.

Explanation:

To determine the probability that a randomly selected incoming senior is allowed to enroll in AP U.S. History, we need to find the number of seniors who have taken either AP World History or AP European History. We can do this by adding the number of students who took AP World History (175), and the number of students who took AP European History (36), and then subtracting the number of students who took both (33).

175 + 36 - 33 = 178

Therefore, out of the 825 incoming seniors, 178 are allowed to enroll in AP U.S. History.

The probability can be calculated by dividing the number of students allowed to enroll (178) by the total number of incoming seniors (825):

P(allowed to enroll) = 178/825 ≈ 0.216 (rounded to three decimal places)