Using Conditional Probabilities Quick Check 1 of 51 of 5 Items Question Which of the following formulas is used to mathematically recognize and explain the conditional probability of event A , given event B ?(1 point) Responses P(A|B)=P(A and B)P(A) 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 A right parenthesis End Fraction P(A and B)=P(A)P(A and B) upper P left parenthesis upper A and upper B right parenthesis equals Start Fraction upper P left parenthesis upper A right parenthesis over upper P left parenthesis upper A and upper B right parenthesis End Fraction P(A and B)=P(A)⋅P(B) upper P left parenthesis upper A and upper B right parenthesis equals upper P left parenthesis upper A right parenthesis times upper P left parenthesis upper B right parenthesis P(A|B)=P(A and B)P(B) 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

Answer 1

The correct formula that mathematically represents the conditional probability of event A given event B is:

\[ P(A|B) = \frac{P(A \text{ and } B)}{P(B)} \]

This means that the conditional probability of event A occurring given that event B has occurred is equal to the probability of both events A and B occurring divided by the probability of event B occurring.

So, the correct response from your options is: P(A|B) = \(\frac{P(A \text{ and } B)}{P(B)}\).