Questions: A spinner with 5 equally sized slices has 2 yellow slices, 2 red slices, and 1 blue slice. Kaitlin spun the dial 500 times and got the following results.
Outcome Yellow Red Blue
Number of Spins 203 187 110
Answer the following. Round your answers to the nearest thousandths.
(a) From Kaitlin's results, compute the experimental probability of landing on blue.
(b) Assuming that the spinner is fair, compute the theoretical probability of landing on blue.
(c) Assuming that the spinner is fair, choose the statement below that is true.
- With a large number of spins, there must be no difference between the experimental and theoretical probabilities.
- 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.
Transcript text: A spinner with 5 equally sized slices has 2 yellow slices, 2 red slices, and 1 blue slice. Kaitlin spun the dial 500 times and got the following results.
\begin{tabular}{|c|c|c|c|}
\hline Outcome & Yellow & Red & Blue \\
\hline Number of Spins & 203 & 187 & 110 \\
\hline
\end{tabular}
Answer the following. Round your answers to the nearest thousandths.
(a) From Kaitlin's results, compute the experimental probability of landing on blue.
$\square$
(b) Assuming that the spinner is fair, compute the theoretical probability of landing on blue.
$\square$
(c) Assuming that the spinner is fair, choose the statement below that is true.
With a large number of spins, there must be no difference between the experimental and theoretical probabilities.
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.
Solution
Solution Steps
Step 1: Calculate the experimental probability of landing on blue.
The experimental probability is the number of times the event occurred divided by the total number of trials. In this case, the spinner landed on blue 110 times out of 500 spins. So, the experimental probability of landing on blue is 110/500 = 0.220.
Step 2: Calculate the theoretical probability of landing on blue.
The theoretical probability is the number of favorable outcomes divided by the total number of possible outcomes. There is 1 blue slice out of a total of 5 slices. Therefore, the theoretical probability of landing on blue is 1/5 = 0.2.
Step 3: Choose the correct statement about the relationship between experimental and theoretical probabilities.
With a large number of spins, the experimental probability should get closer to the theoretical probability. There might be a small difference, but it shouldn't be large. Thus, the correct statement is: 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) 0.220
(b) 0.2
(c) With a large number of spins, there might be a difference between the experimental and theoretical probabilities, but the difference should be small.