Question

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 1

Answer:

0.6

Step-by-step explanation:

Given:

P( Person chosen at random has a B.S. degree), P(C) = 0.5

P( Person chosen at random does not have a B.S. degree), P(C') = 1 - 0.5 = 0.5

P(Student earns more than $100,000) = P(E)

P(Student earns more than $100,000, without going college) = P(E | C') = 0.4

P(Student earns more than $100,000, with college degree) = P(E | C) = 0.6

Now,

P(at least a B.S. degree | earns more than $100,000), P(C | E)

using Baye's theorem

we have

P(C | E) = $\frac{P(C)\timesP(E | C)}{P(C)\timesP(E | C)+P(C')\timesP(E | C')}$

or

P(C | E) = $\frac{0.5\times0.6}{0.5\times0.6+0.5\times0.4}$

or

P(C | E) = $\frac{0.3}{0.5}$

or

P(C | E) = 0.6