Question

In a certain geographic location, 25% of the wage earners have a college degree and 75% do not. Of those who have a college degree, 5% earn more than $100,000 a year. Of those who do not have a college degree, 2% earn more than $100,000 a year. If a wage earner is selected at random, find the probability that she or he earns more than $100,000 a year.

Answer 1

Problem #6443 In a certain geographic location, 25% of the wage earners have a college degree and 75% do not. Of those who have a college degree, 5% earn more than $100,000 a year. Of those who do not have a college degree, 2% earn more than $100,000 a year. If a wage earner is selected at random, find the probability that she or he earns more than $100,000 a year.

Solution Let $H_1$ — be an event that randomly chosen person has a college degree. $H_2$ — does not have a college degree. Then $P(H_1) = 0.25$ and $P(H_2) = 0.75$. Let $A$ be an event that randomly chosen person earns more than $100,000$ a year, then $P(A|H_1) = 0.05$ and $P(A|H_2) = 0.02$. Thus, by law of total probability one can get $P(A) = P(A|H_1)P(H_1) + P(A|H_2)P(H_2) = 0.25 \cdot 0.05 + 0.02 \cdot 0.75 = 0.0275$.

Answer 0.0275.