Question

compare the probability of winning when playing regular defense with the probability of winning when playing prevent defense. draw a conclusion based on your results.
a. ( p(\text{win} | \text{regular}) = 0.76 )
( p(\text{win} | \text{prevent}) = 0.58 )
conclusion: you are more likely to win by playing regular defense.
b. ( p(\text{win} | \text{regular}) = 0.36 )
( p(\text{win} | \text{prevent}) = 0.64 )
conclusion: you are more likely to win by playing regular defense.
c. ( p(\text{win} | \text{regular}) = 0.36 )
( p(\text{win} | \text{prevent}) = 0.64 )
conclusion: you are more likely to win by playing prevent defense.
d. ( p(\text{win} | \text{regular}) = 0.76 )

Explanation:

Step1: Calculate \(P(\text{win}|\text{regular})\)

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). Here, for \(P(\text{win}|\text{regular})\), \(n(\text{win}\cap\text{regular}) = 38\) and \(n(\text{regular})=50\). So \(P(\text{win}|\text{regular})=\frac{38}{50}=0.76\).

Step2: Calculate \(P(\text{win}|\text{prevent})\)

For \(P(\text{win}|\text{prevent})\), \(n(\text{win}\cap\text{prevent}) = 29\) and \(n(\text{prevent}) = 50\). So \(P(\text{win}|\text{prevent})=\frac{29}{50}=0.58\).

Step3: Compare the probabilities

Since \(0.76>0.58\), we conclude that you are more likely to win by playing regular defense.

Answer:

A. \( P(\text{win}|\text{regular}) = 0.76\), \(P(\text{win}|\text{prevent}) = 0.58\). Conclusion: You are more likely to win by playing regular defense.