To determine whether Ron should replace the pitcher or keep the pitcher in based on the given historical data, we need to analyze the win rates associated with each decision.
Here is a step-by-step solution:
1. Identify the given data:
- When Ron replaced the pitcher, the results were:
- Won game: 8 times
- Lost game: 4 times
- Tied game: 2 times
- Total games: 14 times
- When Ron kept the pitcher, the results were:
- Won game: 4 times
- Lost game: 5 times
- Tied game: 1 time
- Total games: 10 times
2. Calculate the win rates for each decision:
- Win rate when replacing the pitcher:
Number of games won after pitcher was replaced = 8
Total number of games when pitcher was replaced = 14
[tex]\[
\text{Win rate replace} = \frac{\text{Number of wins when replaced}}{\text{Total games when replaced}} = \frac{8}{14} \approx 0.5714
\][/tex]
- Win rate when keeping the pitcher:
Number of games won when pitcher was kept = 4
Total number of games when pitcher was kept = 10
[tex]\[
\text{Win rate keep} = \frac{\text{Number of wins when kept}}{\text{Total games when kept}} = \frac{4}{10} = 0.4
\][/tex]
3. Compare the win rates:
- Win rate when replaced: 0.5714
- Win rate when kept: 0.4
4. Decision-making based on win rates:
Since the win rate is higher when Ron replaces the pitcher (0.5714) compared to when he keeps the pitcher in (0.4), it is clear that replacing the pitcher has a higher likelihood of winning the game.
Therefore, the best decision for Ron, aiming to win the game within nine innings, would be to replace the pitcher with a relief pitcher.
Conclusion:
A. Ron should replace the pitcher with a relief pitcher.
