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To solve this problem, we need to use a tree diagram to map out all possible paths through the maze and calculate the probability that a participant will not win any money. Here is a step-by-step breakdown of how to approach this:

### 1. Analyzing the Maze
- The maze has multiple forks where participants must choose a path.
- Each fork splits into two possible paths.
- There are three possible outcomes:
  1. "Nothing" (no prize)
  2. "$" (prize area worth $10)
  
### 2. Drawing the Tree Diagram
To create the tree diagram:
1. **First Fork**: The participant can go either left or right.
   - Left (L1)
   - Right (R1)
   
2. **Second Forks**: If the participant took the left path (L1), it splits into:
   - Left (L2) leading to "Nothing"
   - Right (R2) leading to "$"
   
   If the participant took the right path (R1), it splits into:
   - Left (L3) leading to "Nothing"
   - Right (R3) leading to "$"

### 3. Possible Paths
Given the structure:
1. Path 1: L1 → L2 → "Nothing"
2. Path 2: L1 → R2 → "$"
3. Path 3: R1 → L3 → "Nothing"
4. Path 4: R1 → R3 → "$"

### 4. Calculating Probabilities
- There are 4 possible paths, and each is equally likely because participants choose paths randomly at each fork.
- Probability for each path: $ \frac{1}{4} $

### 5. Desired Probability
- We need to find the probability that a participant **will not win any money**.
- This happens if they end up on "Nothing":
  1. Path 1: L1 → L2 → "Nothing"
  2. Path 3: R1 → L3 → "Nothing"
- There are 2 "Nothing" paths out of 4 total paths.

### 6. Final Probability
- Probability of not winning any money: 
\[
\frac{\text{Number of "Nothing" paths}}{\text{Total number of paths}} = \frac{2}{4} = \frac{1}{2} = 0.5
\]

### 7. Conclusion
- The probability that a participant will not win any money is **0.5** or **50%**.

Would you like a more detailed explanation or have any questions?

### 5 Related Questions
1. What is the expected monetary value for a participant entering the maze?
2. How would the probability change if more forks were added to the maze?
3. If it costs $5 to enter the maze, what is the net expected gain or loss for a participant?
4. How can the area model be used to solve this problem?
5. What would be the probability of winning money if the paths were not equally likely?

### Tip
When solving probability problems involving equally likely outcomes, always ensure to identify all possible outcomes and the ones that meet the desired condition.

Participants in a corn maze choose paths at random, and you need to calculate the probability that a participant will not win any money. It costs $5 to enter, and they win $10 if they exit at a prize area.

Learn how to calculate the probability that a participant will not win any money in a corn maze, where paths are chosen randomly. Using a tree diagram, this problem illustrates key concepts in probability. Suitable for students in Grades 7-9.

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