# Probability Tree Diagrams as Puzzles!

I’m a tree hugger – a probability tree hugger!

I like to draw pictures when solving problems – sketches of the situation, graphs, dots and boxes. I’ll draw whatever it takes to help me wrap my brain around what’s going on.

So the first time I saw a probability tree diagram, I was in love.

### Theory and Concepts vs. Tools

There’s more to calculating probabilities than drawing probability tree diagrams. Some people like to understand the theory first and to apply tools and tricks later.

And some people find  grasping the concept easier if they use a tool – like probability trees.

I’m not going to attempt to explain how to calculate probabilities here. Instead, I’m going to treat probability tree diagrams as puzzles.

In other words, were going to play with the tool, without even touching on the theory or concepts.

Which means if you can follow these puzzle rules, you can do the probability tree diagrams.

And when (or if) you need to use them for calculating probabilities, you’ll know how!

### A New Kind of Puzzle

Here are the rules for the probability tree diagram puzzle:

1. All of the branches coming from a particular node have to add up to one.
2. All of the “leaves” on the very end have to add up to one.
3. Each leaf at the very end is calculated by multiplying all numbers down the branches leading to that leaf.

If you want a more detailed explanation, along with examples – check out this downloadable reference I made.

A completed probability tree looks like this:

It can also have more than two branches like this:

### Do them – or create them!

I’ve created a worksheet with 11 different puzzles on it. Enjoy it yourself or share it with your kids (tweet this).

But you can do more – have them create their own probability tree diagram puzzles. In the process ask them:

1. What’s the minimum amount of information you can put on each probability tree diagram puzzle for it to be solvable?
2. Does this change if you add more branches?
3. Do you have to have at least one piece of information on each “level”?

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### 2 Responses to Probability Tree Diagrams as Puzzles!

1. Alice Petillo says:

Is there a reason why the second example hasn’t been corrected/updated?

• Bon says:

Yes, Alice, there are a few.

1. I’m crazy busy with lots of other things.
2. This is a minor error that only one person in 2.5 years has noticed.
3. The important content of the piece is error-free.
4. I have a list of things to do on the blog that has about 130 things on it.
5. It’s nice to let others discover the error too.

All things taken together, it’s just not even on the list to get fixed.

However, I appreciate you commenting about it so that others will know that when they find the error, they aren’t crazy. 🙂

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