Answer :
To determine the best defensive strategy based on the given data, we need to calculate the probability of winning for each defense strategy and then compare those probabilities.
1. Calculate the probability of winning with regular defense:
The probability of winning with regular defense can be calculated using the formula:
[tex]\[ P(\text{win} | \text{regular defense}) = \frac{\text{number of wins with regular defense}}{\text{total number of games with regular defense}} \][/tex]
From the table:
[tex]\[ \text{Number of wins with regular defense} = 38 \][/tex]
[tex]\[ \text{Total number of games with regular defense} = 50 \][/tex]
Hence:
[tex]\[ P(\text{win} | \text{regular defense}) = \frac{38}{50} = 0.76 \][/tex]
2. Calculate the probability of winning with prevent defense:
The probability of winning with prevent defense can be calculated using the formula:
[tex]\[ P(\text{win} | \text{prevent defense}) = \frac{\text{number of wins with prevent defense}}{\text{total number of games with prevent defense}} \][/tex]
From the table:
[tex]\[ \text{Number of wins with prevent defense} = 29 \][/tex]
[tex]\[ \text{Total number of games with prevent defense} = 50 \][/tex]
Hence:
[tex]\[ P(\text{win} | \text{prevent defense}) = \frac{29}{50} = 0.58 \][/tex]
3. Compare the probabilities and draw a conclusion:
The calculated probabilities are:
[tex]\[ P(\text{win} | \text{regular defense}) = 0.76 \][/tex]
[tex]\[ P(\text{win} | \text{prevent defense}) = 0.58 \][/tex]
Comparing these probabilities, [tex]\(0.76 > 0.58\)[/tex], which indicates that the probability of winning is higher when playing regular defense.
Therefore, the conclusion is:
[tex]\[ \text{You are more likely to win by playing regular defense.} \][/tex]
So, the correct answer is:
[tex]\[ \text{B. } P(\text{win} | \text{regular defense}) = 0.76 \text{ and } P(\text{win} | \text{prevent defense}) = 0.58 \\ \text{Conclusion: You are more likely to win by playing regular defense.} \][/tex]
1. Calculate the probability of winning with regular defense:
The probability of winning with regular defense can be calculated using the formula:
[tex]\[ P(\text{win} | \text{regular defense}) = \frac{\text{number of wins with regular defense}}{\text{total number of games with regular defense}} \][/tex]
From the table:
[tex]\[ \text{Number of wins with regular defense} = 38 \][/tex]
[tex]\[ \text{Total number of games with regular defense} = 50 \][/tex]
Hence:
[tex]\[ P(\text{win} | \text{regular defense}) = \frac{38}{50} = 0.76 \][/tex]
2. Calculate the probability of winning with prevent defense:
The probability of winning with prevent defense can be calculated using the formula:
[tex]\[ P(\text{win} | \text{prevent defense}) = \frac{\text{number of wins with prevent defense}}{\text{total number of games with prevent defense}} \][/tex]
From the table:
[tex]\[ \text{Number of wins with prevent defense} = 29 \][/tex]
[tex]\[ \text{Total number of games with prevent defense} = 50 \][/tex]
Hence:
[tex]\[ P(\text{win} | \text{prevent defense}) = \frac{29}{50} = 0.58 \][/tex]
3. Compare the probabilities and draw a conclusion:
The calculated probabilities are:
[tex]\[ P(\text{win} | \text{regular defense}) = 0.76 \][/tex]
[tex]\[ P(\text{win} | \text{prevent defense}) = 0.58 \][/tex]
Comparing these probabilities, [tex]\(0.76 > 0.58\)[/tex], which indicates that the probability of winning is higher when playing regular defense.
Therefore, the conclusion is:
[tex]\[ \text{You are more likely to win by playing regular defense.} \][/tex]
So, the correct answer is:
[tex]\[ \text{B. } P(\text{win} | \text{regular defense}) = 0.76 \text{ and } P(\text{win} | \text{prevent defense}) = 0.58 \\ \text{Conclusion: You are more likely to win by playing regular defense.} \][/tex]
