To determine which defensive strategy is better for the coach's football team, we need to compare the probabilities of winning when using regular defense versus prevent defense. Let's go through the analysis step by step.
### Step 1: Probability of Winning with Regular Defense
The first strategy to analyze is the regular defense. We have the following data:
- Number of games won with regular defense: 42
- Number of games played with regular defense: 50
To find the probability of winning with regular defense, we use the formula for probability:
[tex]\[ P(\text{Win | Regular Defense}) = \frac{\text{Number of wins with regular defense}}{\text{Total number of games with regular defense}} \][/tex]
So,
[tex]\[ P(\text{Win | Regular Defense}) = \frac{42}{50} = 0.84 \][/tex]
### Step 2: Probability of Winning with Prevent Defense
The second strategy is the prevent defense. We have the following data:
- Number of games won with prevent defense: 35
- Number of games played with prevent defense: 50
To find the probability of winning with prevent defense, we use the formula for probability:
[tex]\[ P(\text{Win | Prevent Defense}) = \frac{\text{Number of wins with prevent defense}}{\text{Total number of games with prevent defense}} \][/tex]
So,
[tex]\[ P(\text{Win | Prevent Defense}) = \frac{35}{50} = 0.7 \][/tex]
### Step 3: Comparison and Conclusion
Now that we have the probabilities:
- Probability of winning with regular defense: 0.84
- Probability of winning with prevent defense: 0.7
Comparing these probabilities, we find that [tex]\( 0.84 > 0.7 \)[/tex].
### Conclusion
Based on the calculated probabilities, the football team has a higher probability of winning when using the regular defense strategy (0.84) compared to the prevent defense strategy (0.7). Therefore, it is statistically better for the coach to use the regular defense when the team is ahead late in the game.
