Let's Do Tree Diagrams

One Tool Used in Probability is a tree diagram. There are two types of tree diagrams the first is a diagram with replacement. The second type is a diagram without replacement. Today we will be working on a tree diagram with replacement.
Ready? Let's get started......

Lets say you have three balls, one blue and two red. So we draw two sepaarate lines to show the two possibilities.







 So if a red is pulled out  and there is still a two third chance of pulling another red. If a blue is pulled out there is a one third chance it will be pulled out again.

Now let us work on the second line. If a blue is pulled pulled first and then replaced it had a one third chance. It then has a two third chance of a red being pulled next and a one third chance of a blue being pulled again.

Still with me?
Now to figure out the probability
Look at your diagram you have created and multiply....yes it is that simple
Okay so
The probability of getting two reds in a row is two thirds multiplied by two thirds so four ninths.
next the probability of pulling a red then a blue is two thirds multiplied by one third which equals two ninths the same goes for pulling a red and then a blue.
Lastly the probability of pulling out two blue balls is one third multiplied by one third which equals one ninth.
Tah Dah! You just did Probability! WOOHOO!!!