johnnyBuz

This can be sometimes confusing. Let's start with a definition, followed by an example.

A conditional probability is defined as a probability of an event given the occurrence of another event. In contrast, an unconditional probability is a probability of an event occurring without restrictions. Another way to think of it is - conditional has some dependency whereas unconditional is independent.

So, if an expectation is such that a conditional event A takes place given an occurrence of another event B, AND the product of these two events, AxB, creates an unconditional result then this is known as the 'total probability rule'.

For example, in hypothetical terms, let's say google expects to earn $50/share from increased advertising revenue if their total page views exceed 100 trillion times next year. The probability of this happening is .001. And there is a .30 probability that a start-up next year will come up with a better search algorithm than google. The total probability that google will meet its earnings target if the page views are exceeded AND a start-up fails to deliver is 0.0007.

Does this help.