Dependent Events on a Tree Diagram

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.

What Is Probability?

A probability is a measure of how likely (how probable) an event is to happen. A probability is expressed as a number between 0 (impossible) and 1 (certain). The formula for finding a probability is shown below:

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