Answer :
To determine which defensive strategy is better in terms of winning probability, we can compare the probabilities of winning under each strategy.
### Step-by-Step Solution:
#### 1. Understand the Data
From the table provided:
- For "Regular Defense":
- Number of wins: 42
- Number of losses: 8
- Total games played: 50
- For "Prevent Defense":
- Number of wins: 35
- Number of losses: 15
- Total games played: 50
#### 2. Calculate the Probability of Winning under Each Strategy
The probability of winning under a given strategy can be calculated as the number of wins divided by the total number of games played with that strategy.
##### Probability of Winning with Regular Defense:
[tex]\[ \text{Probability of Win (Regular Defense)} = \frac{\text{Number of Wins (Regular Defense)}}{\text{Total Games (Regular Defense)}} = \frac{42}{50} \][/tex]
[tex]\[ \text{Probability of Win (Regular Defense)} = 0.84 = 84\% \][/tex]
##### Probability of Winning with Prevent Defense:
[tex]\[ \text{Probability of Win (Prevent Defense)} = \frac{\text{Number of Wins (Prevent Defense)}}{\text{Total Games (Prevent Defense)}} = \frac{35}{50} \][/tex]
[tex]\[ \text{Probability of Win (Prevent Defense)} = 0.7 = 70\% \][/tex]
#### 3. Compare the Probabilities
The probability of winning when using the "Regular Defense" is 84%, while the probability of winning when using the "Prevent Defense" is 70%.
#### 4. Draw a Conclusion
Since 84% (Regular Defense) is higher than 70% (Prevent Defense), the data suggests that playing the "Regular Defense" provides a better chance of winning compared to playing the "Prevent Defense". Therefore, the "Regular Defense" strategy is the better option for the coach based on the given outcomes.
### Step-by-Step Solution:
#### 1. Understand the Data
From the table provided:
- For "Regular Defense":
- Number of wins: 42
- Number of losses: 8
- Total games played: 50
- For "Prevent Defense":
- Number of wins: 35
- Number of losses: 15
- Total games played: 50
#### 2. Calculate the Probability of Winning under Each Strategy
The probability of winning under a given strategy can be calculated as the number of wins divided by the total number of games played with that strategy.
##### Probability of Winning with Regular Defense:
[tex]\[ \text{Probability of Win (Regular Defense)} = \frac{\text{Number of Wins (Regular Defense)}}{\text{Total Games (Regular Defense)}} = \frac{42}{50} \][/tex]
[tex]\[ \text{Probability of Win (Regular Defense)} = 0.84 = 84\% \][/tex]
##### Probability of Winning with Prevent Defense:
[tex]\[ \text{Probability of Win (Prevent Defense)} = \frac{\text{Number of Wins (Prevent Defense)}}{\text{Total Games (Prevent Defense)}} = \frac{35}{50} \][/tex]
[tex]\[ \text{Probability of Win (Prevent Defense)} = 0.7 = 70\% \][/tex]
#### 3. Compare the Probabilities
The probability of winning when using the "Regular Defense" is 84%, while the probability of winning when using the "Prevent Defense" is 70%.
#### 4. Draw a Conclusion
Since 84% (Regular Defense) is higher than 70% (Prevent Defense), the data suggests that playing the "Regular Defense" provides a better chance of winning compared to playing the "Prevent Defense". Therefore, the "Regular Defense" strategy is the better option for the coach based on the given outcomes.
