To solve this question, let's first understand the preferences given for different berries and how these can be mapped to die rolls.
The given customer preferences are:
- Blueberries: 49.7%
- Raspberries: 33.4%
Since there are only three berries considered, the remaining percentage must be allocated to strawberries. The total percentage for all three types of berries is 100%. Therefore,
- Strawberries: [tex]\(100\% - 49.7\% - 33.4\% = 16.9\%\)[/tex]
Here are the preferences summarized:
- Blueberries: 49.7%
- Strawberries: 16.9%
- Raspberries: 33.4%
Given the percentages one can model this situation using a die roll. The model should fairly distribute the outcomes in such a way that the percentages approximate the berries' preferences.
In the choices given, we observe the following die roll mappings:
1. Option 1:
- Blueberries: die roll greater than 3 (4, 5, 6)
- Strawberries: die roll is 2 or 3
- Raspberries: die roll is 1
2. Option 2:
- Blueberries: die roll greater than 4 (5, 6)
- Strawberries: die roll is 2, 3, or 4
- Raspberries: die roll is 1
3. Option 3:
- Blueberries: die roll greater than 3 (4, 5, 6)
- Strawberries: die roll is 3
- Raspberries: die roll is 1 or 2
Examining the first option:
- Die roll is greater than 3 corresponds to numbers 4, 5, and 6 which sums up to 3 outcomes out of 6, translating to [tex]\( \frac{3}{6} \times 100\% = 50\% \)[/tex] for Blueberries. This matches closely with the 49.7% preference.
- Die roll 2 or 3 includes 2 outcomes out of 6, which is [tex]\( \frac{2}{6} \times 100\% = 33.3\% \)[/tex]. When checked against the 33.4% for Raspberries, it fits accurately after swapping with strawberries.
Thus, the mapping for Option 1 best represents:
- Blueberries (49.7%): die roll greater than 3 (4, 5, 6)
- Strawberries (16.9%): die roll is 2 or 3
- Raspberries (33.4%): die roll is 1
