Try Again

Your answer is incorrect.
(a): Your answer is incorrect.
The spinner below shows equally sized slices. Ashley spun the dial times and got the following results.
Outcome Grey White Black
Number of Spins
Fill in the table below. Round your answers to the nearest thousandth.
(a) Assuming that the spinner is fair, compute the theoretical probability of landing on grey.

(b) From Ashley's results, compute the experimental probability of landing on grey.

(c) Assuming that the spinner is fair, choose the statement below that is true:

As the number of spins increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.

The experimental and theoretical probabilities must always be equal.

As the number of spins increases, we expect the experimental and theoretical probabilities to become farther apart.

1 answer

To answer the questions about the spinner and the probabilities, we need to consider the context provided:

(a) Theoretical Probability of Landing on Grey

Assuming that the spinner is fair and has equally sized slices for Grey, White, and Black, we need to calculate the theoretical probability of landing on Grey.

If there are 3 equally sized slices (Grey, White, and Black), the calculation for the theoretical probability is:

\[ P(\text{Grey}) = \frac{\text{Number of Grey slices}}{\text{Total number of slices}} = \frac{1}{3} \approx 0.333 \] Rounded to the nearest thousandth: 0.333

(b) Experimental Probability of Landing on Grey

To calculate the experimental probability of landing on Grey, we need the results from Ashley's spins. Let's assume she spun the spinner a total of \( n \) times and landed on Grey \( g \) times.

The experimental probability can be calculated using the formula:

\[ P(\text{Grey}) = \frac{\text{Number of times Grey was landed on}}{\text{Total number of spins}} = \frac{g}{n} \]

Since the specific numbers from the spins are not provided in your prompt, you would replace \( g \) and \( n \) with Ashley's actual results.

(c) True Statement About Experimental and Theoretical Probabilities

Based on the Law of Large Numbers, we can say:

As the number of spins increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.

This indicates that with more spins, the experimental probability (observed outcome) tends to converge toward the theoretical probability (expected outcome).

If you provide Ashley's results (number of spins for each outcome), I could help further with calculation of the experimental probability.