To find [tex]\( P(B \mid A) \)[/tex], we need to use the definition of conditional probability. The conditional probability of [tex]\( B \)[/tex] given [tex]\( A \)[/tex], denoted as [tex]\( P(B \mid A) \)[/tex], is defined as:
[tex]\[ P(B \mid A) = \frac{P(B \cap A)}{P(A)} \][/tex]
Here, [tex]\( P(B \cap A) \)[/tex] represents the probability that both events [tex]\( A \)[/tex] and [tex]\( B \)[/tex] occur simultaneously. However, since events [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are mutually exclusive, they cannot happen at the same time. Therefore, [tex]\( P(B \cap A) = 0 \)[/tex].
Given:
- [tex]\( P(A) = 0.55 \)[/tex]
- [tex]\( P(B) = 0.07 \)[/tex]
- Events [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are mutually exclusive: [tex]\( P(B \cap A) = 0 \)[/tex]
Substituting [tex]\( P(B \cap A) \)[/tex] and [tex]\( P(A) \)[/tex] into the formula for conditional probability:
[tex]\[ P(B \mid A) = \frac{P(B \cap A)}{P(A)} = \frac{0}{0.55} \][/tex]
Since any number divided by a positive number is zero:
[tex]\[ P(B \mid A) = 0 \][/tex]
Thus, the conditional probability [tex]\( P(B \mid A) \)[/tex] is [tex]\( \boxed{0} \)[/tex].
