To answer the question about the estimated probability that at least one of the next four fish Roxanne catches will be a perch, we need to follow several steps.
Step 1: Analyze the simulation results to determine the frequency of each type of fish.
From the table, we can extract a list of all fish numbers:
```
7888, 2635, 2961, 2053, 2095,
4526, 6994, 4348, 3087, 7282,
8323, 3579, 3840, 6839, 5168,
0585, 1780, 3363, 7683, 2921
```
Step 2: Categorize the digits as per Roxanne's encoding:
- Trout: 0, 1, 2 (30%)
- Bass: 3, 4 (20%)
- Perch: 5 (10%)
- Other Fish: 6, 7, 8, 9 (40%)
Step 3: Count each type of fish from the digits in the table:
- Trout: 20
- Bass: 18
- Perch: 8
- Other Fish: 34
Step 4: Calculate the total number of fish:
Total number of fish = 80
Step 5: Determine the proportions of each type of fish:
- Proportion of Trout: [tex]\( \frac{20}{80} = 0.25 \)[/tex] (25%)
- Proportion of Bass: [tex]\( \frac{18}{80} = 0.225 \)[/tex] (22.5%)
- Proportion of Perch: [tex]\( \frac{8}{80} = 0.1 \)[/tex] (10%)
- Proportion of Other Fish: [tex]\( \frac{34}{80} = 0.425 \)[/tex] (42.5%)
Step 6: Calculate the probability that at least one of the next four fish Roxanne catches will be a perch.
- The probability of not catching a perch in a single catch is [tex]\( 1 - 0.1 = 0.9 \)[/tex].
- The probability of not catching a perch in each of the next four catches is [tex]\( (0.9)^4 = 0.6561 \)[/tex].
- Therefore, the probability of catching at least one perch in the next four catches is:
[tex]\[
1 - 0.6561 = 0.3439 \approx 34.39%
\][/tex]
So, the estimated probability that at least one of the next four fish Roxanne catches will be a perch is approximately 34.39%. Therefore, the closest answer is:
B. [tex]\(35 \%\)[/tex]
