Question

In the senior year of a high school graduating class of 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. Randomly select a student from the class and find the probabilities of the following events. (a) A person enrolled in psychology takes all three subjects. (b) A person not taking psychology is taking both history and mathematics

Answer 1

The probability of finding a person enrolled in psychology that takes all three subjects is 10%, and the probability of finding a person not taking psychology that is taking both history and mathematics is 22%.

Probabilities

To find the probability of A) a person enrolled in psychology that takes all three subjects, and B) a person not taking psychology that is taking both history and mathematics; the following calculations must be made:

• A) 10/100 x 100 = X
• 0.1 x 100 = x
• 10 = X

• B) 22/100 x 100 = X
• 0.22 x 100 = X
• 22 = X

Therefore, the probability of finding a person enrolled in psychology that takes all three subjects is 10%, and the probability of finding a person not taking psychology that is taking both history and mathematics is 22%.

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