To answer your questions, we first need to calculate the probabilities based on the data Kira collected from her spins.
(a) Experimental Probability of Landing on Grey
To calculate the experimental probability of landing on grey, you'll need the number of spins that resulted in grey and the total number of spins. The formula for experimental probability is:
\[ P(\text{Grey}) = \frac{\text{Number of Spins on Grey}}{\text{Total Number of Spins}} \]
Assuming Kira spun the dial a number of times and got a specific count for each color, you'll need to use those specific counts to calculate the probabilities.
Example Calculation:
- Assume Kira had:
- Number of Spins on White: 5
- Number of Spins on Grey: 3
- Number of Spins on Black: 2
Total Spins = 5 + 3 + 2 = 10
Then the experimental probability of landing on grey would be:
\[ P(\text{Grey}) = \frac{3}{10} = 0.300 \]
Rounding to the nearest thousandth gives 0.300.
(b) Theoretical Probability of Landing on Grey
To compute the theoretical probability of landing on grey, we need to know how many equally sized slices are on the spinner. Without that specific information, a general formula can be provided if there are, for example, 3 equal slices:
\[ P(\text{Grey}) = \frac{\text{Number of Grey Slices}}{\text{Total Number of Slices}} \]
If there is 1 grey slice in a spinner divided into 3 equally sized slices, the theoretical probability would be:
\[ P(\text{Grey}) = \frac{1}{3} \approx 0.333 \]
You would round this to the nearest thousandth, resulting in 0.333.
(c) Selection of True Statement
The correct statement is:
As the number of spins increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.
This reflects the understanding that with a larger sample size, the experimental results will reflect the theoretical probabilities more closely due to the law of large numbers.
If you provide the actual numbers from the experiment, I can give you more precise answers.