To answer your questions, we need to calculate both the theoretical and experimental probabilities of landing on green.
Theoretical Probability
The theoretical probability of landing on green is determined by the ratio of the number of green sections on the spinner to the total number of sections on the spinner. We need to know how many total sections (colors) are on the spinner. From the results provided:
- Blue: 14
- Green: 12
- Orange: 6
- Purple: 10
- Red: 10
- Yellow: 8
Total spins: \(60\)
Total sections/colors on the spinner: \(14 + 12 + 6 + 10 + 10 + 8 = 60\)
Now, since we have the experimental counts (not the exact sections on the spinner), we'll determine the probability based on these counts. Let's assume that the spinner divides the sections proportionately to the experimental counts.
If we assume the total outcomes are \(60\) (combined counts), let's calculate the theoretical probability as follows:
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Determine the total number of sections: \[ \text{Total sections} = 6 \] (Blue, Green, Orange, Purple, Red, Yellow)
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The number of green sections = 1 section.
So the theoretical probability of landing on green, assuming equal sections, would be: \[ P(\text{green}) = \frac{\text{Number of green sections}}{\text{Total sections}} = \frac{1}{6} \]
Experimental Probability
The experimental probability of landing on green is calculated based on the actual results of Victoria's spins.
\[ P(\text{green}) = \frac{\text{Number of times green was landed on}}{\text{Total number of spins}} = \frac{12}{60} \]
Now, simplify \(\frac{12}{60}\) to get: \[ P(\text{green}) = \frac{12 \div 12}{60 \div 12} = \frac{1}{5} \]
Summary of Answers
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Theoretical Probability of landing on green: \( \frac{1}{6} \)
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Experimental Probability of landing on green: \( \frac{1}{5} \)
Question 2
The statement can be completed as follows: "The theoretical probability of landing on green is less than the experimental probability of landing on green."