To find the probability that a randomly selected medal from the container is not a gold medal, we need to follow a systematic approach. Let's break it down step-by-step. ### Step 1: Understand the Total Number of Medals First, we need to determine the total number of medals in the container. The container has: - 30 gold medals - 22 silver medals - 18 bronze medals To find the total number of medals, we add these quantities together: \[ \text{Total Medals} = \text{Gold Medals} + \text{Silver Medals} + \text{Bronze Medals} \] \[ \text{Total Medals} = 30 + 22 + 18 = 70 \] ### Step 2: Determine the Number of Non-Gold Medals Next, we need to find out how many medals are not gold. This includes both silver and bronze medals. We can calculate this as follows: \[ \text{Non-Gold Medals} = \text{Silver Medals} + \text{Bronze Medals} \] \[ \text{Non-Gold Medals} = 22 + 18 = 40 \] ### Step 3: Calculate the Probability The probability of an event is defined as the number of favorable outcomes divided by the total number of possible outcomes. In this case, the favorable outcomes are the non-gold medals, and the total outcomes are the total number of medals. The probability \( P \) that a randomly selected medal is not a gold medal can be calculated using the formula: \[ P(\text{Not Gold}) = \frac{\text{Number of Non-Gold Medals}}{\text{Total Number of Medals}} \] Substituting the values we found: \[ P(\text{Not Gold}) = \frac{40}{70} \] ### Step 4: Simplify the Probability Now, we simplify the fraction \( \frac{40}{70} \): \[ P(\text{Not Gold}) = \frac{40 \div 10}{70 \div 10} = \frac{4}{7} \] ### Conclusion: Correct Option Thus, the probability that a randomly selected medal is not a gold medal is \( \frac{4}{7} \). Therefore, the correct option is: **C. 4/7** ### Step 5: Explanation of Other Options Now, let's briefly discuss why the other options are incorrect: - **A. 9/35**: This option is incorrect because it does not represent the correct ratio of non-gold medals to total medals. The calculation of non-gold medals was not considered properly. - **B. 11/35**: This option is also incorrect. It suggests a different count of non-gold medals or total medals, which does not align with our calculations. - **D. 3/7**: This option is incorrect as well. It implies a different probability calculation that does not reflect the actual number of non-gold medals. ### Revision Summary - Total medals = 30 (gold) + 22 (silver) + 18 (bronze) = 70. - Non-gold medals = 22 (silver) + 18 (bronze) = 40. - Probability of not selecting a gold medal = \( \frac{40}{70} = \frac{4}{7} \). - Correct answer is option C: \( \frac{4}{7} \). This thorough breakdown should help you understand how to approach probability questions involving different categories of items.