In the senior year of a high school graduating class at 100 students, 42 studied mathematics, 68 studied psychology, 54 studied history, 22 studied both mathematics and history, 25 studied both mathematics and psychology, 7 studied history but neither mathematics nor psychology, 10 studied all three subjects, and 8 did not take any of the three. If a student is selected at random, find the probability that

a.) a person enrolled in psychology takes all three subjects
b.) a person not taking psychology is taking both history and mathematics.

I'll get you started, and you can finish:

For (a) there are 68 people studying psych, and since there are 10 studying all three subjects that means that 10 out of these 68 are studying all three subjects.

For (b) there are 22 taking history and math, which includes the 10 who are taking alll three. So 22-10 = 12 are taking history and math but not psych. The total number of people not takling psych is 100-68 = 32.

You should be able to finish these two problem up now. Post back with your final answers and we'll check them for you.