Applied Mathematics

Probability Theory

What is conditional probability?

Conditional probability is often phrased as “event A occurs given that event B has occurred.” The common notation is a vertical line, or A | B (said as “A given B”). Thus, P (A | B) denotes the probability that event A will occur given that event B has occurred already.
Since there is always room for improvement—even in probability—conditional probability incorporates the idea that once more information becomes available, the probability of further outcomes can be revised. For example, if a person brings a car in for an oil change every 3,000 miles, it can be calculated that there is a probability of 0.9 that the service on the car will be completed within two hours. But if the car is brought in during a seatbelt recall, the probability of getting the car back in two hours might be reduced to 0.6. This is the conditional probability of getting the car back in two hours if there is a seatbelt recall taking place.



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