1. **State the problem:** We have data on advanced degrees earned by sex and type. We want to find probabilities related to doctor's degrees and gender. 2. **Data summary:** - Male Bachelor's: 90 - Female Bachelor's: 120 - Male Master's: 212 - Female Master's: 121 - Male Doctor's: 111 - Female Doctor's: 100 3. **Total degrees awarded:** $$\text{Total} = 90 + 120 + 212 + 121 + 111 + 100 = 754$$ 4. **(a) Probability of a doctor's degree:** Total doctor's degrees = $111 + 100 = 211$ $$P(\text{Doctor's}) = \frac{211}{754} \approx 0.280$$ 5. **(b) Probability the person is female:** Total females = $120 + 121 + 100 = 341$ $$P(\text{Female}) = \frac{341}{754} \approx 0.452$$ 6. **(c) Probability the person is female given a doctor's degree:** $$P(\text{Female} | \text{Doctor's}) = \frac{\text{Female Doctor's}}{\text{Total Doctor's}} = \frac{100}{211} \approx 0.474$$ 7. **(d) Probability the person has a doctor's degree given female:** $$P(\text{Doctor's} | \text{Female}) = \frac{\text{Female Doctor's}}{\text{Total Female}} = \frac{100}{341} \approx 0.293$$