Develop a tree diagram for tossing two, eight-sided gaming dice to figure out how many possibilities there are. Discuss the purpose of using such a visual in working out probability.
To develop a tree diagram for tossing two eight-sided gaming dice, we can start by considering all the possible outcomes for the first dice throw, followed by all the possible outcomes for the second dice throw.
Here is the tree diagram for tossing two eight-sided gaming dice:
Dice 1 Dice 2
| |
------- -------
| | | |
1 1 1 1,2,3,4,5,6,7,8
| | | |
1 2 1 1,2,3,4,5,6,7,8
| | | |
1 3 1 1,2,3,4,5,6,7,8
. . . .
. . . .
. . . .
1 8 1 1,2,3,4,5,6,7,8
| | | |
2 1 2 1,2,3,4,5,6,7,8
| | | |
2 2 2 1,2,3,4,5,6,7,8
. . . .
. . . .
. . . .
8 7 8 1,2,3,4,5,6,7,8
| | | |
8 8 8 1,2,3,4,5,6,7,8
In the above tree diagram, the first dice (Dice 1) can have values from 1 to 8, and for each value of Dice 1, the second dice (Dice 2) can also have values from 1 to 8. We list all possible combinations of the two dice values by following each branch in the tree.
The purpose of using a tree diagram is to easily visualize and list all the possible outcomes or combinations of events. It helps in organizing and understanding the different possibilities in a systematic manner. In the context of probability, tree diagrams are useful for calculating probabilities of compound events. By counting the total number of outcomes and the number of favorable outcomes in the tree diagram, we can determine probabilities by dividing the number of favorable outcomes by the total number of outcomes.