Conditional Probability Formula

A

A conditional probability takes the form of P(A | B) = P(AB) / P(B), where P(B) does not equal 0. Note that this is just a rearranged form of the formula for joint probability.

The formula for conditional probability is given by option A: P(A | B) = P(AB) / P(B).

Conditional probability is a concept in probability theory that measures the probability of an event A occurring given that another event B has already occurred. In other words, it calculates the probability of event A happening, assuming that event B has already taken place.

Let's break down the components of the formula:

• P(A | B): This represents the conditional probability of event A occurring given that event B has already occurred. The vertical bar "|" is read as "given" or "conditional on."
• P(AB): This represents the joint probability of both events A and B occurring simultaneously. It is the probability that events A and B happen together.
• P(B): This represents the probability of event B occurring, regardless of whether event A has occurred or not.

The formula states that to calculate the conditional probability of event A given event B, you divide the joint probability of events A and B (P(AB)) by the probability of event B (P(B)).

Intuitively, this formula can be understood as follows: The probability of event A occurring given that event B has already occurred is equal to the probability that both events A and B occur together (joint probability) divided by the probability of event B alone.

Therefore, option A correctly represents the formula for conditional probability: P(A | B) = P(AB) / P(B).