1. **State the problem:** We are given the number of touchdowns Luis scored in football games and the frequency of each number of touchdowns. We need to create a probability distribution table. 2. **Given data:** | Touchdowns scored ($X$) | 0 | 1 | 2 | 3 | | Number of games ($f$) | 6 | 10 | 7 | 5 | 3. **Formula for probability:** The probability of each outcome is given by: $$P(X = x) = \frac{\text{Number of games with } x \text{ touchdowns}}{\text{Total number of games}}$$ 4. **Calculate total number of games:** $$6 + 10 + 7 + 5 = 28$$ 5. **Calculate probabilities for each touchdown count:** - For $X=0$: $$P(0) = \frac{6}{28} = \frac{3}{14} \approx 0.2143$$ - For $X=1$: $$P(1) = \frac{10}{28} = \frac{5}{14} \approx 0.3571$$ - For $X=2$: $$P(2) = \frac{7}{28} = \frac{1}{4} = 0.25$$ - For $X=3$: $$P(3) = \frac{5}{28} \approx 0.1786$$ 6. **Probability distribution table:** | Touchdowns scored ($X$) | 0 | 1 | 2 | 3 | |-------------------------|---|---|---|---| | Probability ($P(X)$) | 0.2143 | 0.3571 | 0.25 | 0.1786 | 7. **Check sum of probabilities:** $$0.2143 + 0.3571 + 0.25 + 0.1786 = 1.0$$ This confirms the probabilities are valid. **Final answer:** The probability distribution table is as shown above.