Peter Washington
PhD candidate in Bioengineering at Stanford University.
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Independent Probabilities

Independent Probabilities_image

A fundamental probability rule is:

P(A ∩ B) = P(A | B)P(B) = P(B | A)P(A)

If events A and B are independent, meaning that one event occurring does not affect whether the other event occurs, then this formula can be simplified to:

P(A ∩ B) = P(A)P(B) 

An example of two independent events are two consecutive fair coin flips: the outcome of one coin flip does not affect the other coin flip outcome. By contrast, two dependent events would be driving intoxicated and getting into a car crash: the probability of getting into a car crash significantly increases if someone is driving drunk.