The correct answer is: A. P(B) Ã P(A/B).
Conditional probability is the probability of event A occurring given that event B has already occurred. It is calculated by dividing the probability of both events occurring by the probability of event B occurring.
In other words, P(A|B) = P(A and B) / P(B).
Option A is the correct answer because it is the formula for conditional probability. Option B is incorrect because it is the formula for joint probability. Option C is incorrect because it is the formula for marginal probability. Option D is incorrect because it is not a valid formula for probability.
Here is a more detailed explanation of each option:
- Option A: P(B) Ã P(A/B)
This is the formula for conditional probability. Conditional probability is the probability of event A occurring given that event B has already occurred. It is calculated by dividing the probability of both events occurring by the probability of event B occurring.
In other words, P(A|B) = P(A and B) / P(B).
- Option B: P(B) Ã P(A)
This is the formula for joint probability. Joint probability is the probability of both events A and B occurring. It is calculated by multiplying the probability of event A occurring by the probability of event B occurring.
In other words, P(A and B) = P(A) Ã P(B).
- Option C: P(A) + P(B)
This is the formula for marginal probability. Marginal probability is the probability of event A occurring, regardless of whether or not event B occurs. It is calculated by adding the probability of event A occurring and the probability of event B occurring, minus the probability of both events occurring.
In other words, P(A) = P(A and B) + P(A and not B).
- Option D: None of these
This is the correct answer because it is not a valid formula for probability.