Blogs/Independent Probabilities

Independent Probabilities

peter.washington Jul 15 2021 1 min read 261 views

Stanford ML PhD

Fundamentals Prob. and Stats
Independent Probabilities 2021.png

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.

 

Learn and practice this concept here: 

https://mlpro.io/problems/independent-probability/