QM and Probability Theory

I've been preparing myself for over a week for my Statistics and Probability exam. I understand if you think that  I'm reaaaally stupid, but I feel great going to an exam and knowing that your head will not stop thinking about number and formulas, knowing that last night the only things in your dream were the formulas you  just learned...that sort of gives me confidence =).

I think at this point , my brain is thinking about numbers all the time, I have always been a big fan of Poker, specially the good old Texas Hold'em version. But, at this point I should not be invited to any game or I will stop the whole thing just to calculate all the probabilities Ive got to win the hand.....living hell. Proabilities are all over my head, however I'm not a the ''dreaming with formulas'' level.....that will take me another 3 days and a lot more caffeine. =).

Anyway, around two days ago I bumped into the know concept of complete set of events, defined over a probability space. You know...the sort of thing you find everyday while eating bread or not.

Right after this useful concept, there is the theorem that allows you to express any event, as the sum of conditional probabilities. I mean, if  $\{n_1, n_2, n_3,\dots , n_N \}$is a set of complete events in a probability space, then for any event A holds:

This is when I thought, this look just like the formula used in QM to decompose any vector to a given basis. That is:

Where, , is a basis for the space. (for the sake of simplicity, a finite one.) 

The good thing is that this similarity will make it easier to remember. However, I realized that the resemblance is only aesthetic. I mean, the vectors in QM do not represent probabilities themselves. you always need to multiply them by their complex conjugate, and only then you will obtain a probability (a probability density will be more precise). So  I can always use the fact that I remember one to construct the other, but I have to be aware that they are not the same formula written with a different notation. 

I have the vague notion that multiplying the second formula by its complex conjugate will give me the first formula...but I haven't worked it out.....yet