Editing Probability (section)

===Compound/What are the odds of several things happening?===
The probability of any mutually exclusive events happening is the sum of the probabilities of each event. That is, since you cannot simultaneously roll a 1, 2, or 3 on a [[d6]], they are mutually exclusive events. The probability of rolling a 1, 2 or 3 on a [[d6]] is [[File:Probability Eq1.png|frameless|upright=1.25]].

For multiple events happening in a specific order over multiple trials, (for instance, the odds of rolling a d20 and getting four natural twenties in a row) take all the odds and multiply them together. So, the odds of rolling one natural twenty is 1/20. Two in a row? That's 1*1 / 20*20, or 1/400. Three in a row? 1/8000. Four? 1/160000. Getting a 9 on a d10 and then getting a 75 or higher on a d100 is 1/10*25/100 or 25/1000 or 1/40.

What does that mean for your chances of rolling a nat 20 if you just rolled one? Absolutely fucking nothing. Your dice don't remember what you just rolled, and if they did they wouldn't care. This is known as the Lack of Memory property, and is obvious from each event (roll) being independent. In notation, it would be [[File:Probability Eq2.png|frameless|upright=0.35]], or "the probability of rolling a 20, given that a 20 has already been rolled." 

Keep in mind that this is NOT the same as saying "rolling a d20 two times and getting at least one natural 20." The probability of this happening is actually 9.75%. Why? See below.