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, and 33 took both. Given this information, determine the probability a randomly selected incoming senior is allowed to enroll in AP U. S. History.

About 0.22

Explanation:

There are two sets:

Set W of incoming seniors who took AP World History, and Set E of incoming seniors who took AP European History

And there is a subset, which is the intersection of those two sets:

Subset W ∩ E of senior students who took both.

The incoming seniors who are allowed to enroll in AP U. S. History, call them the subset S, is the set of those students that belong to W or E or both W ∩E.

By property of sets:

S = W + E - W∩E = 175 + 36 - 33 = 178

Then, 178 out of 825 incoming seniors took one or both courses, and the desired probability of a randomly selected incoming senior is allowed to enroll in AP U. S. History is:

178/825 = 0.21576 ≈ 0.22