Tree Diagram

Have any of you heard of a tree diagram? Or what it is used for? Well we learned about them today and well they were confusing at first, but actually really fun after I understood how they worked. Here is an example of a Tree Diagram. They are used to help calculate probabilities and helps you understand how it works. So I hope this picture doesn't scare you right off the back because it is actually easier than it looks. 

Lets do one that will go along with this graph so you can have a visual aid. Suppose there is vending bouncy ball machine. In this machine there are 3 Red Balls, 2 Green Balls, and 1 White Ball. There is this mother named Sally who has two kids, twins to be exact and she wants to get them each a ball. What is the probability of getting a red, and then a green ball in that order?

So in the FIRST STAGE

On the line going up to red we would put 3/6
On the line that goes to the white one we would put 1/6
Finally on the line that goes to the green we would write 2/6

Now if you were to add up all the numerators you should get 6
1+2+3=6

Now the SECOND STAGE would be written like this, since there is one ball being taken out each time we have to take that into account.

Red to Red = 2/5
Red to White = 1/5
Red to Green = 2/5

Add the numerators up and you get 5

White to Red = 3/5
White to White = 0/5
White to Green = 2/5

Add the numerators up and you get 5

Green to Red = 3/5
Green to White = 1/5
Green to Green = 1/5

Add the numerators up and you get 5

Now for the THIRD STAGE you have

RR 6/30 + GG 2/30 = 8/30 = 4/15

The probability of Sally getting a red and then a green ball is 4/15