Tree Diagram Sample Space

For representing sample space, we are using tree diagrams, venn diagrams and graphs. A tree diagram is used to find out the elements of sample space of any experiment. The tree diagram is also used to determine the probability of individual outcomes within the sample space. In this article, we are going to see tree diagrams for sample space example problems.

Example 1 - Tree Diagram Sample Space

Illustrate the sample space for tossing of coin and rolling a die.

Solution:

There are 2 faces in a coin. That is, head and tail.

There are 6 faces in a die. That is, 1, 2, 3, 4, 5 and 6.

The tree diagram for this experiment is,

This is the tree diagram for sample space of given data.

The sample space is,

{H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}

The probability for each of outcomes is,

1/2 × 1/6 = 1/12

Example 2 - Tree Diagram Sample Space

There are three children are in a family. How many outcomes are in sample space that represents the sex of children? Assume that probability of male (M) and probability of female (F) are each 1/2 .

Solution:

The tree diagram for this given information is,

This is the tree diagram for sample space of given data.

The sample space for this tree diagram is,

{MMM, MMF, MFM, MFF, FMM, FMF, FFM, FFF}

There are totally 8 outcomes in sample space.

The probability for each outcome in this sample space is,

1/2 × 1/2 × 1/2 = 1/8

Example 3 - Tree Diagram Sample Space

A bag contains red, lavender and yellow color balloons. A ball is picked and coin is tossed at random at same time. Illustrate the sample space tree diagram.

Solution:

The tree diagram for this experiment is,

This is the tree diagram for sample space of given data.

The sample space for this tree diagram is,

{(Red, Head), (Red, Tail), (Lavender, Head), (Lavender, Tail), (Yellow, Head), (Yellow, Tail)}

There are totally 6 outcomes in sample space.