Use a tree diagram to find the sample space and the total number of possible outcomes.
event: Miniature golf, Laser tag, Roller skating
time: 1:00 p.m.– 3:00 p.m., 6:00 p.m.– 8:00 p.m
To create a tree diagram to find the sample space and total number of possible outcomes for the given events and times, we will start by listing the options for each event and time separately.
Event options:
- Miniature golf
- Laser tag
- Roller skating
Time options:
- 1:00 p.m. – 3:00 p.m.
- 6:00 p.m. – 8:00 p.m.
Now, let's construct the tree diagram by combining the event and time options:
Miniature golf
/ \
1:00 p.m. – 3:00 p.m. 6:00 p.m. – 8:00 p.m.
| |
Laser tag Roller skating
/ \ / \
1:00 p.m. – 3:00 p.m. 1:00 p.m. – 3:00 p.m. 1:00 p.m. – 3:00 p.m.
| |
6:00 p.m. – 8:00 p.m. 6:00 p.m. – 8:00 p.m.
By following the branches in the tree diagram, we can see all the possible combinations of events and times.
Sample space (possible outcomes):
- Miniature golf at 1:00 p.m. – 3:00 p.m.
- Miniature golf at 6:00 p.m. – 8:00 p.m.
- Laser tag at 1:00 p.m. – 3:00 p.m.
- Laser tag at 6:00 p.m. – 8:00 p.m.
- Roller skating at 1:00 p.m. – 3:00 p.m.
- Roller skating at 6:00 p.m. – 8:00 p.m.
Total number of possible outcomes: 6
To create a tree diagram to find the sample space and total number of possible outcomes, we can start by listing all the events and times as branches of the tree.
1. Write "Events" as the first level of the tree diagram.
2. Under "Events," write the three events: Miniature golf, Laser tag, Roller skating.
3. Add a second level under each event to represent the two time options: 1:00 p.m.–3:00 p.m. and 6:00 p.m.–8:00 p.m.
4. Now, add branches under the time options to list all the possible outcomes.
Tree Diagram:
```
Events
|--- Miniature golf
| |--- 1:00 p.m.–3:00 p.m.
| |--- 6:00 p.m.–8:00 p.m.
|
|--- Laser tag
| |--- 1:00 p.m.–3:00 p.m.
| |--- 6:00 p.m.–8:00 p.m.
|
|--- Roller skating
| |--- 1:00 p.m.–3:00 p.m.
| |--- 6:00 p.m.–8:00 p.m.
```
By filling in the branches, we can see that each event has two possible time options, resulting in a total of six possible outcomes.
Sample Space:
1. Miniature golf at 1:00 p.m.–3:00 p.m.
2. Miniature golf at 6:00 p.m.–8:00 p.m.
3. Laser tag at 1:00 p.m.–3:00 p.m.
4. Laser tag at 6:00 p.m.–8:00 p.m.
5. Roller skating at 1:00 p.m.–3:00 p.m.
6. Roller skating at 6:00 p.m.–8:00 p.m.
Therefore, the sample space consists of these six outcomes, and there are six possible outcomes in total.