Suppose Joan has a fair four-sided die with sides that are numbered 1, 2, 3, and 4.Image attribution: CC BY NC 3.0 by CK-12After she rolls it 20 times, Joan finds that she’s rolled the number 3 six times. What is the empirical probability that Joan rolls a 3? 6% 20% 25% 30%

Suppose Joan has a fair four-sided die with sides that are numbered 1, 2, 3, and 4.Image attribution: CC BY NC 3.0 by CK-12After she rolls it 20 times, how many times does she roll the number 3? 3 5 6 It is impossible to tell.

Suppose Joan has a fair four-sided die with sides that are numbered 1, 2, 3, and 4.Image attribution: CC BY NC 3.0 by CK-12After 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 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. 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 without also knowing how many times the other numbers appeared. 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.

A six-sided die is rolled ( 10 ) (10) times, and the results are listed below. 3 3 , 4 4 , 1 1 , 1 1 , 2 2 , 6 6 , 6 6 , 5 5 , 6 6 , 3 3 What is the experimental probability of rolling a ( 3 ) (3) ?

What is the probability of NOT rolling a four when rolling a six sided die?

A standard six-sided die is rolled repeatedly until either a six comes up or two fives come up in a row. Find the probability that the die is rolled at least four times.