Talia uses the spinner shown below for an experiment.

Question

A circular spinner is divided into 3 equal sections labeled yellow, purple, and orange.

Talia 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 Talia's experiment?

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

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

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

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

Answer 1

The correct answer is:

A. If Talia increases her number of spins, the observed frequencies will likely get closer to \( \frac{1}{3} \).

This is based on the law of large numbers, which states that as the number of trials (in this case, spins of the spinner) increases, the observed frequencies will tend to get closer to the expected probabilities. In this scenario, since the spinner is equally divided into three sections, the expected probability for each color is \( \frac{1}{3} \). Talia's observed frequencies are 6 purple, 1 yellow, and 5 orange, which is skewed due to a limited number of spins (12 spins). However, with more spins, it is expected that the frequencies will approximate the true probabilities more closely.