1. **Problem Statement:** Yuri has four sets of cards (A, B, C, D) with different numbers on them. He chooses one set and picks a card from it 600 times with replacement. He gets the number 1 exactly 118 times. We need to find which set he most likely chose. 2. **Understanding the problem:** The probability of picking number 1 from a set is the number of cards with 1 divided by the total number of cards in that set. 3. **Calculate probabilities of picking 1 from each set:** - Set A: Cards are \{1,2,3,4\} total 4 cards, number of 1's = 1 $$P_A = \frac{1}{4} = 0.25$$ - Set B: Cards are \{1,2,3\} total 3 cards, number of 1's = 1 $$P_B = \frac{1}{3} \approx 0.3333$$ - Set C: Cards are \{1,1,2\} total 3 cards, number of 1's = 2 $$P_C = \frac{2}{3} \approx 0.6667$$ - Set D: Cards are \{1,2,3,3,4\} total 5 cards, number of 1's = 1 $$P_D = \frac{1}{5} = 0.2$$ 4. **Calculate the experimental probability from Yuri's picks:** - Number of times 1 was picked = 118 - Total picks = 600 $$P_{exp} = \frac{118}{600} \approx 0.1967$$ 5. **Compare experimental probability with theoretical probabilities:** - $|P_{exp} - P_A| = |0.1967 - 0.25| = 0.0533$ - $|P_{exp} - P_B| = |0.1967 - 0.3333| = 0.1366$ - $|P_{exp} - P_C| = |0.1967 - 0.6667| = 0.47$ - $|P_{exp} - P_D| = |0.1967 - 0.2| = 0.0033$ 6. **Conclusion:** The smallest difference is with Set D, so Yuri most likely chose Set D. **Final answer:** Yuri most likely chose **Set D**.