# Conditional Probability - Mathematics
Data Science for Political and Social Phenomena
Author: Guillaume Redoulès

# Conditional Probability

This is defined as the probability of an event occurring, assuming that one or more other events have already occurred. Two events, A and B are considered to be independent if event A has no effect on the probability of event B (i.e. P(B|A)=P(A)).

If events A and B are not independent, then we must consider the probability that both events occur. This can be referred to as the intersection of events A and B, defined as P(A∩B) = P(B|A)P(A). We can then use this definition to find the conditional probability by dividing the probability of the intersection of the two events (A∩B) by the probability of the event that is assumed to have already occurred (event A):

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

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