I have the problem and the answers as well that the prof has given the class, i'm trying to work backwards to figure out how he solved it. Would appreciate if anyone could show me how he got the numbers (answers are highlighted) as all he gave was a sort explanation.
- Suppose that the probability of a worker receiving the minimum wage is 10%. Of workers who receive the minimum wage, 50% are in low-income households. Of workers who receive more than the minimum wage, 20% are in low-income households.
(a) What is the probability that a random household has low income?
Composing the 2x2 table of joint probabilities and adding up the entries gives 0.05 + 0.18 = 0.23 or 23%
(b) If you are in a low-income household, what is the probability that you receive the minimum wage?
The conditional probability is 0.05/.23 = 21.74%.