1. **State the problem:** We have a survey table of students categorized by gender and their preferred relaxation method: reading or listening to music. | Gender | Read | Listen to Music | |--------|------|----------------| | Female | 87 | 94 | | Male | 68 | 110 | We need to find the probability that a randomly selected student who is female relaxes by listening to music. 2. **Formula used:** The conditional probability formula is $$P(\text{Listen to Music} \mid \text{Female}) = \frac{P(\text{Listen to Music and Female})}{P(\text{Female})}$$ 3. **Calculate total females:** $$\text{Total Females} = 87 + 94 = 181$$ 4. **Calculate probability:** $$P(\text{Listen to Music} \mid \text{Female}) = \frac{94}{181}$$ 5. **Simplify fraction if possible:** 94 and 181 have no common factors other than 1, so fraction is already simplified. 6. **Final answer:** The probability that a randomly selected female student relaxes by listening to music is $$\boxed{\frac{94}{181} \approx 0.519}\text{ or }51.9\%.$$