Question

suppose joan has a fair four - sided die with sides that are numbered 1, 2, 3, and 4. 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. 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. 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 joans experience with this die because there is only a very weak link between the relative frequency of an event and the theoretical probability. d. we cannot draw any conclusions from joans experience with this die without also knowing how many times the other numbers appeared.

Explanation:

Step1: Calculate theoretical probability

For a fair four - sided die, the theoretical probability of rolling a 2 is $P(2)=\frac{1}{4}= 0.25$.

Step2: Calculate relative frequency

Joan rolled the die $n = 2000$ times and rolled a 2, $x = 187$ times. The relative frequency of rolling a 2 is $f=\frac{187}{2000}=0.0935$.

Step3: Analyze the result

The relative frequency $0.0935$ is quite different from the theoretical probability $0.25$. This calls into question whether the die is fair.

Answer:

A. 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.