The probability that an individual without a college education earns more than $100,000 is 0.2, whereas...

The probability that an individual without a college education earns more than $100,000 is 0.2, whereas the probability that a person with a B.S. or higher degree earns more than $100,000 is 0.6. The probability that a person chosen at random has a B.S. degree is 0.5. What is the probability that a person has at least a B.S. degree if it is known that he or she earns more than $100,000? (Round your answer to four decimal places.)

Expert Solution

P(earns more than $100000 | without college education) = 0.2

P(earns more than $100000 | with a B.S. or higher degree) = 0.6

P(has a B.S. degree) = 0.5

P(earns more than $100000) = P(earns more than $100000 | without college education) * P(without college education) + P(earns more than $100000 | with a B.S. or higher degree) * P(has a B.S. degree)

= 0.2 * (1 - 0.5) + 0.6 * 0.5

= 0.4

P(at least a B.S. degree | earns more than $100,000) = P(earns more than $100000 | with a B.S. or higher degree) * P(has a B.S. degree) / P(earns more than $100000)

= 0.6 * 0.5 / 0.4

= 0.75

orchestra answered 1 year ago

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