Question 1193990: 1. Two students are randomly selected from a statistics class, and it is observed whether or not they suffer from math anxiety. How many total outcomes are possible?
a. Draw a tree diagram for this experiment.
b. Draw a Venn diagram.
c. List all the outcomes included in each of the following events. Indicate which are simple and which are compound events.
i. Both students suffer from math anxiety.
ii. Exactly one student suffers from math anxiety.
iii. The first student does not suffer and the second suffers from math anxiety.
iv. None of the students suffers from math anxiety.
Answer by parmen(42)   (Show Source):
You can put this solution on YOUR website! **1. Total Outcomes**
* Each student can have two possible outcomes:
* S: Suffers from math anxiety
* N: Does not suffer from math anxiety
* For two students, the total number of possible outcomes is 2 * 2 = 4.
**a. Tree Diagram**
```
Start
/ \
S N
/ \ / \
S N S N
```
* The tree diagram visually represents the possible outcomes for each student and their combinations.
**b. Venn Diagram**
* Create two overlapping circles.
* One circle represents the first student, the other represents the second student.
* Within each circle, divide it into two sections: S (suffers) and N (does not suffer).
* The overlapping region represents the outcome where both students suffer from math anxiety.
**c. List of Outcomes**
* **i. Both students suffer from math anxiety:** {SS} (Simple event)
* **ii. Exactly one student suffers from math anxiety:** {SN, NS} (Compound event)
* **iii. The first student does not suffer and the second suffers from math anxiety:** {NS} (Simple event)
* **iv. None of the students suffers from math anxiety:** {NN} (Simple event)
**Note:**
* **Simple Event:** An event that consists of a single outcome.
* **Compound Event:** An event that consists of two or more simple events.
Let me know if you'd like to explore any of these concepts further!
|
|
|
