Problem:
On a beach people are wearing sunglasses and people are wearing caps. Some people are wearing both sunglasses and caps. If one of the people wearing a cap is selected at random, the probability that this person is also wearing sunglasses is . If instead, someone wearing sunglasses is selected at random, what is the probability that this person is also wearing a cap?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
If the probability is , that means of the people wearing caps are also wearing sunglasses. This means that people are wearing both caps and sunglasses. The probability of a person wearing sunglasses also wearing a cap is .
Thus, the correct answer is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions