*Originally posted by Nemesio*

**I've just read the Bayesian Theorem article on Wikipedia and don't even understand the chocolate
**

cookie example.

Hold my hand a bit and explain it to me and then explain what it means to be a Bayesian atheist.

I thank you in advance and am,

Appreciatively yours,

Nemesio

Let's start by stating Bayes' Theorem in plain English.

Bayes' Theorem asserts that these two products have an equal value, for any propositions A and B:

1) The probability that A is true whenever B is true, times the probability that B is in fact true.

2) The probability that B is true whenever A is true, times the probability that A is in fact true.

So, there are four things in play in Bayes' Theorem:

a) The probability that A is true, given no information about B, denoted P(A)

b) The probability that B is true, given no information about A, denoted P(B)

c) The probability that A is true, given that B is true, denoted P(A|B)

d) The probability that B is true, given that A is true, denoted P(B|A)

Bayes' Theorem can be applied whenever three of these quantities are known and you wish to determine the fourth. This is why it's usually written as an equation with the unknown quantity on the left and the ratio on the right.

If that framework is clear, then we can go on to apply it to the cookie problem.