c. Ball does not land on a number from 25 through 29 The probability of the event that the ball does not land on a number from 25 through 29 is \( \square \).

To determine the probability that the ball **does not** land on a number from **25 through 29**, we can use the concept of complementary probability. Here's how you can approach it: ### Step-by-Step Solution 1. **Identify the Total Number of Possible Outcomes (N):** Let's assume that the ball can land on any number within a certain range. For the sake of this explanation, we'll denote the total number of possible outcomes as \( N \). 2. **Determine the Number of Unfavorable Outcomes:** The numbers **25 through 29** represent **5** specific outcomes (i.e., 25, 26, 27, 28, 29). 3. **Calculate the Probability of Landing on Numbers 25 through 29:** \[ P(\text{Landing on } 25 \text{ through } 29) = \frac{5}{N} \] 4. **Use Complementary Probability to Find the Desired Probability:** The probability that the ball does **not** land on a number from 25 through 29 is the complement of landing on those numbers. Therefore: \[ P(\text{Does not land on } 25 \text{ through } 29) = 1 - P(\text{Landing on } 25 \text{ through } 29) \] Substituting the value from step 3: \[ P(\text{Does not land on } 25 \text{ through } 29) = 1 - \frac{5}{N} = \frac{N - 5}{N} \] ### Final Answer The probability that the ball does **not** land on a number from **25 through 29** is: \[ \boxed{\frac{N - 5}{N}} \] *Where \( N \) is the total number of possible outcomes.* ### Example If, for example, the ball can land on any number from **1 through 30** (i.e., \( N = 30 \)): \[ P(\text{Does not land on } 25 \text{ through } 29) = \frac{30 - 5}{30} = \frac{25}{30} = \frac{5}{6} \] So, the probability would be \( \frac{5}{6} \) in this case. --- *Please replace \( N \) with the actual total number of possible outcomes specific to your problem to get a numerical probability.*