Make Like A Tree and Leaf Those Worries Behind

Tree diagrams definitely provide the connection that I had always been missing to understand when to multiple events or add them together. 

Making a tree graph is a great way to to physically see how many different outcomes of an event can occur in an organized fashion. Another advantage to tree graphs, is an easy way to find points of misunderstandings. 

Let's use rock, paper, scissors to make a tree diagram for calculating theoretical probability! 

So starting off making the first branches. 

You know you are going to begin with three branches because you have three choices, rock, paper, or scissors. You can choose one out of those three so the probability for each  one is 1/3. Continuing, to see what the probabilities are if you pick any one of those, we have to add in the chances of what your opponent will do! 

So once you pick paper, your partner also has 3 choices of what they can do, rock, paper, or scissors. You would draw 3 branches off of paper and label them P,R,S. Since your partner also had three choices, you label each one with 1/3. 

You repeat these steps for each one until your tree diagram is complete. 

As you are moving across the tree diagram, you multiply each event times itself. 

Paper (1/3) x Paper (1/3) = A tie (1/9)

Paper (1/3) x Scissors (1/3) = Scissors wins (1/9)

Paper (1/3) x Rock (1/3) = Rock wins (1/9)

Scissors (1/3) x Paper = Scissors wins (1/9)

Scissors (1/3) x Scissors = A tie (1/9)

Scissors (1/3) x Rock = Rock wins (1/9)

Rock (1/3) x Paper = Paper wins (1/9)

Rock (1/3) x Scissors = Rock wins (1/9)

Rock (1/3) x Rock = A tie (1/9)

You notice that if you add off these events up (1/9) they come out to (9/9) which equals one. 

When I see branches on a tree, I can see that I should multiply the events together because they are multi-step, they are coming one of after the other, otherwise you probably wouldn't need to tree for it, eh? Well, after you determine a multitude of probabilities, you tend to see that all of your events have the same denominator. This was easier for me to understand that I need to add these numbers together because they are out of 1 essentially. Your probability will always be somewhere in between 0 and 1 because if it wasn't going to happen at all, whatsoever (0) then you wouldn't be willing to risk it. And if it was definitely going to happen (1) you would have done it already! So there you have it, it somewhere between zero and one. 

These end probabilities (1/9) will help you figure out theoretical probabilities. The probability it will end up as tie- (1/9)+(1/9)+(1/9)=(3/9)=*reduced*(1/3)

So you could guess your probability of a tie when playing rock paper scissors! :)
This man has a nice accent to listen to while educating you on how to execute the compilation of tree diagrams. But if your mom keeps asking you what you're doing on the computer and you need a break... you can be mildly entertained by this guy explaining probability. Now say "MOM! I'm calculating probability!" Technically you're still watching something educational and he's a weirdo, sounds like the internet to me!  If you watched it, I'll allow one cat video.. done? Okay back to my blog.