Sure, let me walk you through the solution step-by-step.
1. Hurricane Counts per Trial:
We start by examining each trial to count how many years had hurricanes. A hurricane is represented by the number '1'. Here are the counts for each trial:
- Trial 1: 1 year with a hurricane (2,5,3,2,5,5,1,4,5,2 → one '1' present)
- Trial 2: 5 years with a hurricane (1,1,5,2,2,1,3,1,1,5 → five '1's present)
- Trial 3: 2 years with a hurricane (4,5,4,5,5,4,3,5,1,1 → two '1's present)
- Trial 4: 2 years with a hurricane (1,5,5,5,1,2,2,3,5,3 → two '1's present)
- Trial 5: 1 year with a hurricane (5,1,5,3,5,3,4,5,3,2 → one '1' present)
- Trial 6: 3 years with a hurricane (1,1,5,5,1,4,2,2,3,4 → three '1's present)
- Trial 7: 4 years with a hurricane (2,1,5,3,1,5,1,2,1,4 → four '1's present)
- Trial 8: 2 years with a hurricane (2,4,3,2,4,4,2,1,3,1 → two '1's present)
- Trial 9: 2 years with a hurricane (3,2,1,4,5,3,5,5,1,2 → two '1's present)
- Trial 10: 1 year with a hurricane (3,4,2,4,3,5,2,3,5,1 → one '1' present)
The resulting counts are `[1, 5, 2, 2, 1, 3, 4, 2, 2, 1]`.
2. Count of Trials with At Least 4 Years with a Hurricane:
From the hurricane counts, we see that exactly 2 trials had at least 4 years with hurricanes:
- Trial 2 (5 years with hurricanes)
- Trial 7 (4 years with hurricanes)
3. Total Number of Trials:
The total number of trials conducted is 10.
4. Experimental Probability:
The experimental probability \( P \) that a hurricane would strike the city in at least 4 of the next 10 years is calculated by the formula:
[tex]\[
P = \left(\frac{\text{Number of trials with at least 4 hurricanes}}{\text{Total number of trials}}\right) \times 100\%
\][/tex]
Substituting the values from above:
[tex]\[
P = \left(\frac{2}{10}\right) \times 100\% = 20.0\%
\][/tex]
5. Comparison to Actual Result:
According to the given data, there was actually 1 year out of 10 in which a hurricane struck. To compare this to Rob's simulation, it's simpler to express the number of hurricanes per 10 years:
- Actual result: 1 year with a hurricane over 10 years.
- Rob's simulation result: average of 2 years with hurricanes over 10 years (as out of 10 trials with a singular count per trial).
In percentage terms, this means:
- Actual probability: 10%
- Simulated probability: 20.0%
So, Rob's simulation predicted double the probability of at least 4 hurricanes than what actually happened over the subsequent 10-year period, showing a difference of -10%.
The comparison indicates Rob's simulation overestimates the occurrence of hurricanes when compared to the actual data. This suggests the actual chance was less than what Rob's model predicted.
