Suppose Joan has a fair four-sided die with sides that are numbered 1, 2, 3, and 4. 12 Image attribution: CC BY NC 3.0 by CK-12 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? A. O 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. B. O Joan has demonstrated that this is a fair die, since the relative frequency of rolling a 2 is nearly equal to the theoretical probability. C. 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. D. O We cannot draw any conclusions from Joan's experience with this die without also knowing how many times the other numbers appeared.

MATLAB: An Introduction with Applications
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Chapter1: Starting With Matlab
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Suppose Joan has a fair four-sided die with sides that are numbered 1, 2, 3, and 4.
12
Image attribution: CC BY NC 3.0 by CK-12
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?
A. O 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.
B. O Joan has demonstrated that this is a fair die, since the relative frequency of rolling a 2 is nearly equal to
the theoretical probability.
C. O 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.
D. O We cannot draw any conclusions from Joan's experience with this die without also knowing how many
times the other numbers appeared.
Transcribed Image Text:Suppose Joan has a fair four-sided die with sides that are numbered 1, 2, 3, and 4. 12 Image attribution: CC BY NC 3.0 by CK-12 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? A. O 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. B. O Joan has demonstrated that this is a fair die, since the relative frequency of rolling a 2 is nearly equal to the theoretical probability. C. O 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. D. O We cannot draw any conclusions from Joan's experience with this die without also knowing how many times the other numbers appeared.
Expert Solution
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A is an event associated with a sample space. The theoretical probability is defined as n(A)/n where n is the total outcomes and the condition all outcomes being equally likely applies. The ratio is also the relative frequency. For very sufficiently large n the condition of all outcomes equally likely is relaxed and relative frequency converges to theoretical probability.

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