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(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

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|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(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

Answer 1

The correct formula 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 answer is:

**P(A|B) = P(A and B) / P(B)**