1. **State the problem:** We are given a data table showing how many students play an instrument and/or a sport. We need to find the probability that a randomly chosen student plays both a sport and an instrument. 2. **Data from the table:** - Plays instrument and sport: 8 - Plays sport but not instrument: 2 - Plays instrument but not sport: 5 - Plays neither: 7 3. **Total number of students:** $$8 + 2 + 5 + 7 = 22$$ 4. **Formula for probability:** $$P(\text{sport and instrument}) = \frac{\text{number who play both}}{\text{total number of students}}$$ 5. **Calculate the probability:** $$P = \frac{8}{22}$$ 6. **Simplify the fraction:** $$\frac{8}{22} = \frac{\cancel{2} \times 4}{\cancel{2} \times 11} = \frac{4}{11}$$ 7. **Final answer:** The probability that a randomly chosen student plays both a sport and an instrument is **$\frac{4}{11}$**.