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.
You multiply when you go down a branch (thinning it out); you add when you gather branches together.

The chance of heads this flip followed by tails next flip is $\frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4}$; the chance of either heads or tails this flip is $\frac{1}{2} + \frac{1}{2} = 1$.

If you're confused about whether to add or multiply two probabilities, imagine that they're both $\frac{1}{2}$ and think about whether the result should be $\frac{1}{4}$ or $1$. It'll usually be obvious.