1. **Stating the problem:** We need to analyze how the probability models for Viet, Quinn, and Lucy change when the total numbers in the game increase from 75 to 90, matched with the letters B, I, N, G, and O. 2. **Understanding the original setup:** Originally, there are 75 numbers distributed among the letters B, I, N, G, and O. Each letter corresponds to a subset of numbers. 3. **Effect of increasing total numbers:** When the total numbers increase to 90, the distribution of numbers per letter changes. This affects the probability of drawing a number associated with each letter. 4. **Probability formula:** The probability of drawing a number associated with a letter is: $$ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} $$ 5. **How the models change:** - Since the total number of outcomes increases from 75 to 90, the denominator in the probability fraction increases. - If the number of favorable outcomes per letter remains the same, the probability decreases. - If the favorable outcomes also increase proportionally, the probability might stay the same. 6. **Even/Odd numbers consideration:** If the game involves even/odd number patterns, increasing total numbers may change the count of even or odd numbers per letter, thus changing probabilities. 7. **Summary:** The probability models for Viet, Quinn, and Lucy would change because the total number of possible outcomes increases, altering the probabilities associated with each letter and potentially the distribution of even/odd numbers. **Final answer:** The probabilities change because the total number of numbers increases from 75 to 90, affecting the ratio of favorable outcomes to total outcomes and thus changing the probability models for each player.