Let's carefully examine the problem. We need to determine the probability that event [tex]\(B\)[/tex] occurs given that event [tex]\(A\)[/tex] has already occurred. This probability is known in probability theory as the conditional probability of [tex]\(B\)[/tex] given [tex]\(A\)[/tex], denoted as [tex]\(P(B | A)\)[/tex].
The formula for conditional probability is given by:
[tex]\[ P(B | A) = \frac{P(B \cap A)}{P(A)} \][/tex]
where:
- [tex]\(P(B | A)\)[/tex] is the conditional probability that event [tex]\(B\)[/tex] occurs given that event [tex]\(A\)[/tex] has already occurred.
- [tex]\(P(B \cap A)\)[/tex] is the joint probability that both events [tex]\(B\)[/tex] and [tex]\(A\)[/tex] occur.
- [tex]\(P(A)\)[/tex] is the probability that event [tex]\(A\)[/tex] occurs.
Given this formula, the correct answer is:
[tex]\[ B. \frac{ P (B \cap A)}{ P (A)} \][/tex]
Thus, the answer to the problem is:
[tex]\[ \boxed{2} \][/tex]
So option B is the correct choice.
