Ten percent of students take a distance class and 40 percent are part time; of the part time students 20 percent take a distance class. What is P(part time given distance)?

1. The joint probability is P(part time) times P(distance given part time), which is 0.40 times 0.20. 2. That product is 0.08. 3. The wanted conditional is that joint probability divided by P(distance). 4. So the calculation is 0.08 divided by 0.10. 5. The result is 0.80, so most distance learners are part time students. 6. Answering 0.20 returns the conditional in the other direction, which the different denominators make a different number. _Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 3 "Probability Topics", section 3.3 Two Basic Rules of Probability_