To determine the theoretical probability of landing on green, we first need to define the total number of outcomes and the number of favorable outcomes.
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Theoretical Probability:
- Assume the spinner is evenly divided among the colors. There are 6 colors: Blue, Green, Orange, Purple, Red, and Yellow.
- Therefore, the theoretical probability of landing on green is given by the formula: \[ P(\text{Green}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{6} \]
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Experimental Probability:
- From Victoria's results, the number of times she landed on Green is 12, and she spun the spinner a total of 60 times.
- The experimental probability of landing on green is calculated as: \[ P(\text{Green}) = \frac{\text{Number of times landed on Green}}{\text{Total spins}} = \frac{12}{60} = \frac{1}{5} \]
Now, comparing the two probabilities:
- The theoretical probability of landing on green is \(\frac{1}{6}\).
- The experimental probability of landing on green is \(\frac{1}{5}\).
Now, we can compare these two fractions.
To see which one is larger, we can convert them to a common denominator or compare them directly:
- The common denominator of 6 and 5 is 30.
- Convert \(\frac{1}{6}\) to \(\frac{5}{30}\)
- Convert \(\frac{1}{5}\) to \(\frac{6}{30}\)
Thus, \(\frac{1}{5} > \frac{1}{6}\).
In conclusion:
The theoretical probability of landing on green is \(\frac{1}{6}\), while the experimental probability of landing on green is \(\frac{1}{5}\).
The statement can be completed as follows:
The theoretical probability of landing on green is less than the experimental probability of landing on green.