To determine the most appropriate tool for the simulation, we first need to calculate the win-loss ratio based on the team's performance last season.
The total number of games played last season is the sum of wins and losses:
\[ \text{Total Games} = \text{Wins} + \text{Losses} = 24 + 16 = 40 \]
Now, we can calculate the fraction of games won:
\[ \text{Win Probability} = \frac{\text{Wins}}{\text{Total Games}} = \frac{24}{40} = 0.6 \]
And the fraction of games lost:
\[ \text{Loss Probability} = \frac{\text{Losses}}{\text{Total Games}} = \frac{16}{40} = 0.4 \]
To simulate this with a tool, we should match these probabilities as closely as possible.
Let's evaluate the options:
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A coin with one side representing a win and the other representing a loss: This gives a 50% chance of win and a 50% chance of loss, which does not match the ratio.
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A 6-section spinner with congruent sections, 4 representing a win and 2 representing a loss: This gives a probability of winning of \(\frac{4}{6} \approx 0.67\) and losing \(\frac{2}{6} \approx 0.33\). This is closer, but not accurate.
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A 5-section spinner with congruent sections, 3 representing a win and 2 representing a loss: This gives a probability of winning of \(\frac{3}{5} = 0.6\) and losing \(\frac{2}{5} = 0.4\). This matches the win-loss ratio perfectly.
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An 8-sided die with 5 sides representing a win and 3 sides representing a loss: This gives a win probability of \(\frac{5}{8} = 0.625\) and a loss probability of \(\frac{3}{8} = 0.375\), which is not accurate.
Based on this analysis, the most appropriate tool for simulating the team's wins and losses based on last season's data is:
A 5-section spinner with congruent sections, 3 representing a win and 2 representing a loss.
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