The correct formula used to mathematically recognize and explain the conditional probability of event A given event B is:
\[ P(A|B) = \frac{P(A \text{ and } B)}{P(B)} \]
So the response that corresponds to this formula is:
P(A|B)=P(A and B)P(B)
However, the proper expression for conditional probability is:
upper P left parenthesis upper A vertical bar upper B right parenthesis equals Start Fraction upper P left parenthesis upper A and upper B right parenthesis over upper P left parenthesis upper B right parenthesis End Fraction
This indicates that the formula should be read as:
P(A|B) = P(A and B) / P(B)
Thus, if that is the response as written in your options, that one is the correct answer.