Dependent Events on a Tree Diagram
What Is a Dependent Event?
An event is dependent if its probability is affected by whether or not another event has occured.
A tree diagram can show dependent events.
A Real Example of a Dependent Event on a Tree Diagram
It is easier to understand a dependent event with an example.
Picking Marbles
A bag contains 3 yellow marbles and 2 blue marbles.
Two marbles will be picked from the bag. One marble will be taken out (without being replaced) and then another.
1^{st} Pick
In the 1^{st} pick, a Yellow marble can be chosen or a Blue
The two picks can be drawn on a tree diagram:

There are 3 yellow marbles out of 5. The probability of getting a Yellow marble is ^{3}⁄_{5}.

There are 2 blue marbles out of 5. The probability of getting a Blue marble is ^{2}⁄_{5}.
2^{nd} Pick
The 2^{nd} pick depends on the 1^{st} pick.
1^{st} Pick Is Yellow
Imagine a Yellow marble was picked.
There are now different numbers of yellow and blue marbles than there were in the first pick.

There are 2 yellow marbles out of 4. The probability of getting a Yellow marble is ^{2}⁄_{4}.

There are 2 blue marbles out of 4. The probability of getting a Blue marble is ^{2}⁄_{4}.
1^{st} Pick Is Blue
Imagine a Blue marble was picked.
There are now different numbers of yellow and blue marbles than there were in the first pick.

There are 3 yellow marbles out of 4. The probability of getting a Yellow marble is ^{3}⁄_{4}.

There is 1 blue marble out of 4. The probability of getting a Blue marble is ^{1}⁄_{4}.
We have completed the tree diagram.