Conditional Probability

Conditional probability is used when two or more events are not independent. This means the likelihood of one event is influenced by whether another event occurred. It asks, "If we know A has happened, what's the chance of B also happening?" It's calculated by multiplying the probability of the preceding event by the updated probability of the succeeding, or conditional, event.

Two events are said to be independent if one event occurring does not affect the probability that the other event will occur. However, if one event occurring or not does affect the likelihood that the other event will happen, the two events are said to be dependent, for example, a company's stock price increasing after reporting higher-than-expected earnings. If events are independent, then the probability of some event B is not contingent on what happens with event A, for example, an increase in Apple's shares and a drop in wheat prices.

Conditional probability is often written as the "probability of B given A" and notated as $P(B|A)$.

$$P(B \mid A) = \frac{P(A \cap B)}{P(A)}$$