I have never been very good at probability, and I am confused with this rather simple statement:(adsbygoogle = window.adsbygoogle || []).push({});

"BASIC FACT:

Let E be any event, and F and G be events such that one and only one of the events F and G will occur. Then

P(E) = P(F)*P(E given F) + P(G)*P(E given G)"

Where P(E) = the probability of E occurring. And the same for the others.

To be honest I don't even understand what it is asking me to do procedurally. What does it mean "E given F"? Is that the probability of E occurring if F occurs? Why is that pertinent? More than that I don't understand the reasoning nor do I have any intuitive inkling as to why this expression would yield the correct answer.

Can someone give an example perhaps?

(The book I was given just assumes the reader automatically understands this property).

Any help would be greatly appreciated.

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# Basic Probability question

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