3.2 Exercise 10

Data on incomes and salary ranges for a certain population are analyzed as follows. $S_{1} =$ event annual income is less than $25,000; $S_{2} =$ event annual income is between $25,000 and $100,000; $S_{3} =$ event annual income is greater than $100,000. $E_{1} =$ event did not complete college education; $E_{2} =$ event of completion of bachelor's degree; $E_{3} =$ event of completion of graduate or professional degree program. Data may be tabulated as follows: $P \left(E_{1}\right) = 0 . 65 , P \left(E_{2}\right) = 0 . 30$, and $P \left(E_{3}\right) = 0 . 05$.

1. Determine $P \left(E_{3} S_{3}\right)$.
2. Suppose a person has a university education (no graduate study). What is the (conditional) probability that he or she will make $25,000 or more?
3. Find the total probability that a person's income category is at least as high as his or her educational level.