The Lesson
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}.
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}.