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.

1st Pick

In the 1st 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 35.

  • There are 2 blue marbles out of 5. The probability of getting a Blue marble is 25.

2nd Pick

The 2nd pick depends on the 1st pick.

1st 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 24.

  • There are 2 blue marbles out of 4. The probability of getting a Blue marble is 24.

1st 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 34.

  • There is 1 blue marble out of 4. The probability of getting a Blue marble is 14.

We have completed the tree diagram.

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The slider below another real example of dependent events on a tree diagram.

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See Also

What is probability? What is a dependent event?