Conditional Probability
AdvancedConditional probability is the probability that an event will occur given that another event has already occurred or is known to be true.
Many probabilities depend on circumstances. Conditional probability captures this by asking: what is the chance of A, given that B has happened? It is written as the probability of A given B.
It is calculated by dividing the probability that both events occur by the probability of the condition. For example, suppose 30% of a bank's loans are to higher-risk borrowers, and 10% of those loans default. The probability that a loan is both higher-risk and defaults is 30% multiplied by 10%, or 3%. Turned around, the conditional probability of default given that a loan is higher-risk is 10%.
Conditional probability is central to finance and risk. Credit models estimate default probabilities given a borrower's characteristics. Insurers price policies based on the probability of claims given factors such as age or location. Investors consider the probability of market falls given current conditions.
A common mistake is confusing the probability of A given B with the probability of B given A, which can be very different. Bayes' theorem provides a way to convert one into the other.
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