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4. Understanding Conditional Probability
Conditional probabilities are useful when the probability of one event depends on the outcome of another event. Learn how to use conditional probabilities in this lesson.

Lesson Goal (00:26)
The goal of this lesson is to learn how to calculate conditional probabilities.

Dependent and Independent Events (01:49)
Dependent events are events where the probability of one event is affected by the outcome of another event. For example, an ad campaign for a product is more likely to increase sales for the product if the price of the product is discounted. This is the opposite of independent events, where the outcome of one event does not affect the probability of the other event.

Understanding Conditional Probabilities (02:05)
A conditional probability is the probability of one event occurring given that another event has occurred. We denote this probability using a vertical bar, for example P(AB) is the probability of event A occurring given that event B has already occurred. Note that the conditional probability of A given B (AB) may not be the same as the conditional probability of B given A (BA).
If events A and B are dependent, then the conditional probability will be different from the individual event’s probability. For example, if the probability of A given B is different from the probability of A, this tells us that whether event B occurs influences the probability of event A, which means the events are dependent.

Probabilities of AND Events (03:20)
For two independent events, we can find the probability of both occurring by multiplying their individual probabilities. If the events are dependent, then the probability for the second event should be replaced by the conditional probability given that the first event has occurred. These conditional formulas can also be used for independent events.
This indicates how we can use conditional probabilities to identify if events are dependent or independent. For two independent events, the probability of each event is equal to the conditional probability given that the other event has occurred. If this is not the case, the events are dependent.