Bayes’ Rule is an application of the LOTP with the Conditional Probability rule. Bayes’ theorem describes the probability of an event based on prior knowledge of conditions that might be related to the event.
Let be a partition of and be any event, then
How is bayes rule derived? Apply the basic rule of Conditional Probability, and leverage the fact that AND is commutative. Therefore, you can simplify
You have one fair coin and a biased coin that lands on heads with a probability of 3 4 . A coin is chosen at random and tossed three times. If we observe three heads in a row, what is the probability that the fair coin was chosen?
Solution: The fair coin was chosen The biased coin was chosen 3 heads observed in 3 tosses
We want to find , so we can use Bayes’ Theorem, and calculate
Bayes rule with Conditioning