Question: The "classic" high school probability exercises most of the time ends up in a tree of possibilities that deals with all the scenarios (combinations?) that are possible for a given scenario: be it coin tosses, balls in a jar, anagrams, etc.

But there is something that I always have a had time deciding: when to add and when to multiply quantities under a certain scenario? I see that for each branch of the tree, I can just multiply, but when does addition enters the picture?

![Image 1](https://i.stack.imgur.com/YCYsw.png)

Answer: 
Add for (disjoint) unions, multiply for (independent) intersections.
This is how I try to think of it from non math perspective. Not sure how accurate this is. 

If you think that a compounding event will increase your chance compared to the single event, you use the addition rule. 
Examples:

* Probability of rolling 4 or bigger in a fair dice. (The OR generally
increase your chance as well). The single event is rolling a
number(1/6). The compounding events are rolling 4 or bigger.
Logically, you will have more chance. You add.
* Probability of getting Number cards from a deck of card. You calculate this using 1/52 probability for each card. Generally you
would get a bigger chance if the ask is to drawANY number. Therefore, you add

However, if you think compounding events will decrease your chance compared to the single event, use the multiplication rule. Most of the time you will see the word AND indicating 2 events happening together

Example:

* Probability of getting 2 sixes when rolling a dice 2 times( 6 AND 6). The single event of rolling a six is 1/6. If you need to roll another six the second time, logically, this will be harder. Multiply
* Probability of drawing 3 Aces in a row. This is harder than just drawing 1 ACE. multiply.