What is Conditional Probability?
The conditional
If events A and B are not independent, then the probability of the intersection of A and B (the probability that both events occur) is defined by
P(A and B) = P(A)P(B|A).
From this definition, the conditional probability P(B|A) is easily obtained by dividing by P(A):
The equation above is of course only valid if P(A) is not equal to 0. If the formula looks daunting, the following video will help you understand it. Thanks to Khan Academy. This one is great.
The Bayes’ Theorem gives a way of calculating P(A|B) given the knowledge that P(B|A) has already happened. Bayes’s formula is defined as follows:
Sample problem in my next post.
Good and interesting, except… You break the rule we pain so much to try to inculcate our pupils: You have popped an element in – the letter C, in the terminal formula by Bayes – which you have omited to introduce! Grr! 😉