Questions: The spinner below shows 10 equally sized slices. Lisa spun the dial 40 times and got the following results. Outcome White Grey Black Number of Spins 14 11 15 Fill in the table below. Round your answers to the nearest thousandth. (a) From Lisa's results, compute the experimental probability of landing on white. (b) Assuming that the spinner is fair, compute the theoretical probability of landing on white. (c) Assuming that the spinner is fair, choose the statement below that is true: - With a large number of spins, there might be a difference between the experimental and theoretical probabilities, but the difference should be small. - With a large number of spins, there must be a large difference between the experimental and theoretical probabilities. - With a large number of spins, there must be no difference between the experimental and theoretical probabilities.

The spinner below shows 10 equally sized slices. Lisa spun the dial 40 times and got the following results. Outcome White Grey Black Number of Spins 14 11 15 Fill in the table below. Round your answers to the nearest thousandth. (a) From Lisa's results, compute the experimental probability of landing on white. (b) Assuming that the spinner is fair, compute the theoretical probability of landing on white. (c) Assuming that the spinner is fair, choose the statement below that is true: - With a large number of spins, there might be a difference between the experimental and theoretical probabilities, but the difference should be small. - With a large number of spins, there must be a large difference between the experimental and theoretical probabilities. - With a large number of spins, there must be no difference between the experimental and theoretical probabilities.
Transcript text: The spinner below shows 10 equally sized slices. Lisa spun the dial 40 times and got the following results. \begin{tabular}{|c|c|c|c|} \hline Outcome & White & Grey & Black \\ \hline Number of Spins & 14 & 11 & 15 \\ \hline \end{tabular} Fill in the table below. Round your answers to the nearest thousandth. (a) From Lisa's results, compute the experimental probability of landing on white. $\square$ (b) Assuming that the spinner is fair, compute the theoretical probability of landing on white. $\square$ (c) Assuming that the spinner is fair, choose the statement below that is true: With a large number of spins, there might be a difference between the experimental and theoretical probabilities, but the difference should be small. With a large number of spins, there must be a large difference between the experimental and theoretical probabilities. With a large number of spins, there must be no difference between the experimental and theoretical probabilities.
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Solution

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Solution Steps

Step 1: Calculate the experimental probability of landing on white.

The experimental probability is the ratio of the number of times an event occurred to the total number of trials. In this case, the event is landing on white, which occurred 14 times. The total number of trials is 40 spins. Therefore, the experimental probability of landing on white is 14/40 = 0.35.

Step 2: Calculate the theoretical probability of landing on white.

The theoretical probability is the ratio of the number of favorable outcomes to the total number of possible outcomes. The spinner has 10 equally sized slices. The number of white slices is 4. Therefore, the theoretical probability of landing on white is 4/10 = 0.4.

Step 3: Determine the true statement about the relationship between experimental and theoretical probabilities.

With a large number of trials, the experimental probability should get closer to the theoretical probability. There might still be a small difference, but it should not be large. Therefore, the first statement is true: "With a large number of spins, there might be a difference between the experimental and theoretical probabilities, but the difference should be small."

Final Answer:

(a) 0.350 (b) 0.400 (c) With a large number of spins, there might be a difference between the experimental and theoretical probabilities, but the difference should be small.

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