To solve this problem, we'll need the following information:
- The total number of equally sized slices on the spinner (let’s assume there are three equal parts: grey, white, and black).
- The number of spins Ashley performed and the number of times each outcome occurred.
Since you did not provide specific numbers for the spins or the results, I will help you illustrate how to calculate the probabilities, and I will provide a general guide assuming the spinner is fair and there are three equal parts.
(a) Theoretical Probability of Landing on Grey
Assuming the spinner has three equally sized sections (grey, white, black), the theoretical probability \( P \) of landing on grey is calculated as follows:
\[ P(\text{Grey}) = \frac{\text{Number of Grey Sections}}{\text{Total Number of Sections}} = \frac{1}{3} \approx 0.333 \]
(b) Experimental Probability of Landing on Grey
To compute the experimental probability, we need the number of times Ashley landed on grey and the total number of spins she performed. Let’s say she spun the spinner a total of \( N \) times and landed on grey \( G \) times. The experimental probability \( P_E \) can be calculated as:
\[ P_E(\text{Grey}) = \frac{\text{Number of Times Grey Occurred}}{\text{Total Spins}} = \frac{G}{N} \]
You will need the actual numbers for \( G \) and \( N \) to fill out this part.
(c) True Statement about Probabilities
The correct statement, assuming the spinner is fair and you continue to spin a large number of times, is:
"As the number of spins increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal."
This statement reflects the Law of Large Numbers, which states that as the number of trials increases, the experimental probability (based on actual spins) tends to approach the theoretical probability.
If you provide the number of spins and outcomes, I can help you fill in the table with specific values!