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Concept

**Nodes:**Each node represents a certain event.**Branches:**A branch connects two nodes. Several branches can extend from each node.**Probabilities:**The probability of each outcome is written on its corresponding branch.

Tree diagrams help visualize the probability of events. They can also be used for finding all possible arrangements of a set of elements. Because this type of diagram is commonly used in probability, they are also called **probability trees** or **probability tree diagrams**.

Consider the experiment of flipping a fair coin and then rolling a fair die.

To make the tree diagram, first, the experiment's stages need to be identified. In doing so, include the possible outcomes and probabilities.

**Stage $1.$**Flipping the coin.- The possible outcomes are
*heads*and*tails.* - Each outcome has a probability of $21 .$

- The possible outcomes are
**Stage $2.$**Rolling the die.- The possible outcomes are $1,$ $2,$ $3,$ $4,$ $5,$ and $6.$
- Each outcome has a probability of $61 .$

Using the diagram, the probability of any event can be calculated by multiplying the probabilities of the connected branches. For example, the probability of the coin landing on heads and then rolling a $3$ is given by the product of $21 $ and $61 .$

$P(head and3)=21 ⋅61 ⇕P(head and3)=121 $

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