Question

Tanya uses the spinner shown below for an experiment.



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Tanya spun the spinner 12 times and recorded her results in the table below.



Color Purple Yellow Orange
Frequency 6 1 5


Which of the following statements BEST describes the observed frequencies of Tanya's experiment?


Tanya's observed frequencies prove that the spinner must not be equally spaced.


Tanya's observed frequencies are equal to the expected probability of
1
3
.


If Tanya increases her number of spins, the observed frequencies will likely get farther from
1
3
.


If Tanya increases her number of spins, the observed frequencies will likely get closer to
1
3
.

Answer 1

Answer: If Tanya increases her number of spins, the observed frequencies will likely get closer to 1/3.

Reason: If the spinner is fair each color has probability 1/3, so the expected count in 12 spins is 4 each. Tanya observed 6, 1, and 5 — small random deviations from 4. By the law of large numbers, with more spins the relative frequencies tend to approach the true probability (1/3), so increasing trials will likely make the observed proportions closer to 1/3.