Two spinners with distinct sections of equal area are spun 40 times. Which spinner is most likely to produce actual results closest to the predicted results?
A. a spinner with 2 sections
B. a spinner with 5 sections
C. a spinner with 8 sections
D. a spinner with 10 sections
Answer (1)
The spinner with the most sections is most likely to produce actual results closest to the predicted results.
The spinner with 10 sections is the spinner with the most sections.
Therefore, the spinner with 10 sections is most likely to produce actual results closest to the predicted results.
The answer is the spinner with 10 sections: a s p inn er w i t h 10 sec t i o n s .
Explanation
Understand the problem We have four spinners with different numbers of sections (2, 5, 8, and 10), each spun 40 times. We need to determine which spinner is most likely to produce actual results closest to the predicted results.
Reasoning The more sections a spinner has, the closer the experimental probability will be to the theoretical probability as the number of spins increases. This is due to the law of large numbers.
Conclusion Therefore, the spinner with the most sections, which is the spinner with 10 sections, is most likely to produce actual results closest to the predicted results.
Examples
Imagine you're running a game at a carnival where people spin a wheel to win prizes. If you want the payouts to align closely with your planned budget, using a wheel with more sections will give you more predictable results over many spins. This is because the more sections there are, the more likely the actual outcomes will match the expected probabilities, ensuring fairness and financial stability for your game.
