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:
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B.
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E.
Solution:
Because the probability that a cap-wearing person also wears sunglasses is , it follows that the number of people wearing both caps and sunglasses is . Thus the probability that a randomly chosen person with sunglasses is also wearing a cap is =.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions