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Select the correct answer.

Ron coaches a baseball team. There are three innings left in the game, and the team is losing by four runs. Ron is trying to decide whether to replace the pitcher or keep the pitcher in for another inning. In the past, when losing by four runs, he has replaced the pitcher a total of 14 times and kept the pitcher in a total of 10 times. The table shows the results of these decisions at the end of nine innings.

\begin{tabular}{|l|c|c|}
\hline
& Replaced pitcher & Kept pitcher \\
\hline
Won game & 8 & 4 \\
\hline
Lost game & 4 & 5 \\
\hline
Tied game & 2 & 1 \\
\hline
Total & 14 & 10 \\
\hline
\end{tabular}

Based on the information in the table, if the goal is to win the game in nine innings, should Ron replace the pitcher or keep the pitcher in?

A. There is not enough information to determine if Ron should replace the pitcher or not.
B. Ron should replace the pitcher with a relief pitcher.
C. Replacing or not replacing the pitcher has no advantage.
D. Ron should not replace the pitcher with a relief pitcher.



Answer :

GinnyAnswer
To determine whether Ron should replace the pitcher or keep the pitcher in, we need to evaluate the likelihood of winning the game based on the past outcomes provided in the table.

The table shows the outcomes of Ron's decisions in similar situations. We will calculate the win percentages for both scenarios: replacing the pitcher and keeping the pitcher.

1. Win Percentage when Replacing the Pitcher:
- Ron replaced the pitcher 14 times.
- Out of these 14 times, the team won 8 times.
- Win Percentage = (Number of Wins when Replacing the Pitcher) / (Total Times Replaced the Pitcher)
- Win Percentage = 8 / 14

2. Win Percentage when Keeping the Pitcher:
- Ron kept the pitcher 10 times.
- Out of these 10 times, the team won 4 times.
- Win Percentage = (Number of Wins when Keeping the Pitcher) / (Total Times Kept the Pitcher)
- Win Percentage = 4 / 10

Next, we convert these fractions into percentages:
- Win Percentage when Replacing the Pitcher = (8 / 14) ≈ 0.57 or 57%
- Win Percentage when Keeping the Pitcher = (4 / 10) = 0.40 or 40%

Based on the information given in the table and the calculated win percentages:

- When Ron replaces the pitcher, the team's chance of winning is 57%.
- When Ron keeps the pitcher, the team's chance of winning is 40%.

Thus, the better decision, if Ron's goal is to win the game, would be to replace the pitcher. Therefore, the correct answer is:

B. Ron should replace the pitcher with a relief pitcher.

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