The probability that an individual without a college education earns more than $100,000 is 0.4, 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?

Answer:0.6Step-by-step explanation:Given:P( Person chosen at random has a B.S. degree), P(C) = 0.5P( Person chosen at random does not have a B.S. degree), P(C') = 1 - 0.5 = 0.5P(Student earns more than $100,000) = P(E)P(Student earns more than $100,000, without going college) = P(E | C') = 0.4P(Student earns more than $100,000, with college degree) = P(E | C) = 0.6Now,P(at least a B.S. degree | earns more than $100,000), P(C | E) using Baye's theoremwe haveP(C | E) = [tex]\frac{P(C)\timesP(E | C)}{P(C)\timesP(E | C)+P(C')\timesP(E | C')}[/tex]orP(C | E) = [tex]\frac{0.5\times0.6}{0.5\times0.6+0.5\times0.4}[/tex]orP(C | E) = [tex]\frac{0.3}{0.5}[/tex]orP(C | E) = 0.6