Which of the following formulas is used to mathematically recognize and explain the conditional probability of event A , given event B ?(1 point)

Question

Responses

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|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(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 for conditional probability of event A given event B is:

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

This formula states that the 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.

However, from the options you've provided, none of them fully match this standard representation.

The closest correct option based on your choices seems to be: \[ P(A|B) = \frac{P(A \text{ and } B)}{P(B)} \]

If option is phrased differently than this, please check again and adjust based on the format that matches what's standard for defining conditional probability.