Answer :
To determine whether Ron should replace the pitcher or keep the pitcher if he aims to win the game in nine innings, we need to analyze the probabilities of winning in each scenario. We base this analysis on the given data:
- Ron has replaced the pitcher a total of 14 times.
- Ron has kept the pitcher a total of 10 times.
From the table, we have the following results:
- When Ron replaced the pitcher, his team won 8 times.
- When Ron kept the pitcher, his team won 4 times.
First, let's calculate the winning probability in each scenario:
### Probability of Winning When Replacing the Pitcher
- Number of times Ron's team won when the pitcher was replaced: 8
- Total number of times the pitcher was replaced: 14
The probability of winning when the pitcher is replaced is:
[tex]\[ \text{Probability of Win When Replaced} = \frac{\text{Number of Wins When Replaced}}{\text{Total Times Replaced}} = \frac{8}{14} \][/tex]
### Probability of Winning When Keeping the Pitcher
- Number of times Ron's team won when the pitcher was kept: 4
- Total number of times the pitcher was kept: 10
The probability of winning when the pitcher is kept is:
[tex]\[ \text{Probability of Win When Kept} = \frac{\text{Number of Wins When Kept}}{\text{Total Times Kept}} = \frac{4}{10} \][/tex]
Now let's compare these probabilities:
- [tex]\(\frac{8}{14} \approx 0.571\)[/tex]
- [tex]\(\frac{4}{10} = 0.4\)[/tex]
Clearly, the probability of winning when the pitcher is replaced ([tex]\(\approx 0.571\)[/tex]) is higher than the probability of winning when the pitcher is kept (0.4).
### Conclusion
Based on the higher probability of winning, Ron should replace the pitcher if his goal is to win the game in nine innings. Thus, the best choice is:
Ron should replace the pitcher.
- Ron has replaced the pitcher a total of 14 times.
- Ron has kept the pitcher a total of 10 times.
From the table, we have the following results:
- When Ron replaced the pitcher, his team won 8 times.
- When Ron kept the pitcher, his team won 4 times.
First, let's calculate the winning probability in each scenario:
### Probability of Winning When Replacing the Pitcher
- Number of times Ron's team won when the pitcher was replaced: 8
- Total number of times the pitcher was replaced: 14
The probability of winning when the pitcher is replaced is:
[tex]\[ \text{Probability of Win When Replaced} = \frac{\text{Number of Wins When Replaced}}{\text{Total Times Replaced}} = \frac{8}{14} \][/tex]
### Probability of Winning When Keeping the Pitcher
- Number of times Ron's team won when the pitcher was kept: 4
- Total number of times the pitcher was kept: 10
The probability of winning when the pitcher is kept is:
[tex]\[ \text{Probability of Win When Kept} = \frac{\text{Number of Wins When Kept}}{\text{Total Times Kept}} = \frac{4}{10} \][/tex]
Now let's compare these probabilities:
- [tex]\(\frac{8}{14} \approx 0.571\)[/tex]
- [tex]\(\frac{4}{10} = 0.4\)[/tex]
Clearly, the probability of winning when the pitcher is replaced ([tex]\(\approx 0.571\)[/tex]) is higher than the probability of winning when the pitcher is kept (0.4).
### Conclusion
Based on the higher probability of winning, Ron should replace the pitcher if his goal is to win the game in nine innings. Thus, the best choice is:
Ron should replace the pitcher.
