To find the conditional probability [tex]\( P(B \mid A) \)[/tex], we need to understand what it represents. The conditional probability [tex]\( P(B \mid A) \)[/tex] is the probability that event [tex]\( B \)[/tex] occurs given that event [tex]\( A \)[/tex] has occurred.
First, let's recall that events [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are mutually exclusive. This means that they cannot happen simultaneously. Mathematically, for mutually exclusive events, the intersection of [tex]\( A \)[/tex] and [tex]\( B \)[/tex] is zero:
[tex]\[ P(A \cap B) = 0 \][/tex]
According to the formula for conditional probability:
[tex]\[ P(B \mid A) = \frac{P(A \cap B)}{P(A)} \][/tex]
Substituting the values, we have:
[tex]\[ P(B \mid A) = \frac{0}{P(A)} \][/tex]
Since [tex]\( P(A) \)[/tex] is given as 0.50, we substitute this value in:
[tex]\[ P(B \mid A) = \frac{0}{0.50} = 0 \][/tex]
Therefore, the conditional probability [tex]\( P(B \mid A) \)[/tex] is:
[tex]\[ \boxed{0} \][/tex]
