To determine why Marta has a lower probability of winning than Elena and identify which outcomes could be favorable for Marta, let's analyze the probabilities provided for each potential outcome.
We have the following probabilities for each situation:
- Rolling a sum of 7: \( \frac{1}{6} \approx 0.167 \)
- Rolling a sum of 6: \( \frac{5}{36} \approx 0.139 \)
- Rolling a sum of 2 or a sum of 9: \( \frac{5}{36} \approx 0.139 \)
- Rolling a sum that is greater than 9: \( \frac{1}{6} \approx 0.167 \)
- Rolling a sum that is greater than 2 but less than 5: \( \frac{5}{36} \approx 0.139 \)
Given these probabilities, we'll compare each scenario to evaluate which outcomes Marta could potentially achieve to have her win:
1. Rolling a sum of 7:
- Probability: \( \approx 0.167 \)
- This is the highest probability among the listed outcomes.
2. Rolling a sum of 6:
- Probability: \( \approx 0.139 \)
- Relatively high probability but lower than rolling a sum of 7.
3. Rolling a sum of 2 or a sum of 9:
- Combined probability: \( \approx 0.139 \)
- Combined lower probability, similar to rolling a sum of 6.
4. Rolling a sum that is greater than 9:
- Probability: \( \approx 0.167 \)
- Highest probability equal to rolling a sum of 7.
5. Rolling a sum that is greater than 2 but less than 5:
- Probability: \( \approx 0.139 \)
- Combined lower probability similar to rolling a sum of 6 or sum of 2/9.
From the given choices and probabilities:
The highest probability outcomes are:
1. Rolling a sum of 7 (\( \approx 0.167 \))
2. Rolling a sum that is greater than 9 (\( \approx 0.167 \))
3. Rolling a sum that is greater than 2 but less than 5 (\( \approx 0.139 \))
These outcomes typically present higher or substantial probabilities, potentially explaining Marta's strategy to win despite having a lower probability overall compared to Elena. Therefore, the three favorable outcomes Marta could aim for are:
- Rolling a sum of 7
- Rolling a sum that is greater than 9
- Rolling a sum that is greater than 2 but less than 5
