Suppose Joan has a fair four-sided die with sides that are numbered 1, 2, 3, and

Question

Suppose Joan has a fair four-sided die with sides that are numbered 1, 2, 3, and 4.

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After she rolls it 2,000 times, she finds that she rolled the number 2 a total of 187 times. Which of the following is true?

Joan has demonstrated that this is a fair die, since the relative frequency of rolling a 2 is nearly equal to the theoretical probability.

We cannot draw any conclusions from Joan’s experience with this die because there is only a very weak link between the relative frequency of an event and the theoretical probability.

Joan has provided evidence that calls into question whether or not this is a fair die because the relative frequency of rolling a 2 is quite different than the theoretical probability even after repeating the experiment many times.

We cannot draw any conclusions from Joan’s experience with this die without also knowing how many times the other numbers appeared.

Explanation / Answer

After she rolls it 2,000 times, she finds that she rolled the number 2 a total of 187 times. Which of the following is true?

Joan has demonstrated that this is a fair die, since the relative frequency of rolling a 2 is nearly equal to the theoretical probability.

We cannot draw any conclusions from Joan’s experience with this die because there is only a very weak link between the relative frequency of an event and the theoretical probability.

Joan has provided evidence that calls into question whether or not this is a fair die because the relative frequency of rolling a 2 is quite different than the theoretical probability even after repeating the experiment many times.

We cannot draw any conclusions from Joan’s experience with this die without also knowing how many times the other numbers appeared.

probabilty of getting 2 = 1/4 =0.25

Relative frequency of 2 =187

theoretical probability = 2000 *0.25 =500

187 is quite different than the theoretical probability 500.

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