Build the method
An equally likely random-digit model works only when the mapping matches the required chance. To represent probability 0.2, assign two of ten digits to success and eight to failure. Digits 0 through 2 contain three digits, so that inclusive range would incorrectly represent probability 0.3.
Worked example
Suppose one hundred null repetitions produce statistic counts 4,8,20,28,20,12,8 at −3 through 3. For a preplanned upper-tail test with observed value 2, the simulated p-value is (12+8)/100=0.20. Include ties because values equal to the observation are at least as extreme.
Compare the alternatives
For a two-sided question under an appropriate symmetric null statistic, both corresponding tails may matter. For a one-sided upper question, adding a lower tail changes the event. The alternative must be selected before seeing the result; choosing whichever direction looks favorable changes error rates.
Avoid a specific trap
Two fair dice have thirty-six equally likely ordered pairs. Their eleven possible sums are not equally likely: seven has six pairs while two has one. A simulation should roll two independent outcomes, not draw uniformly from the list of sums.
Transfer check with explanation
Transfer: increasing simulated repetitions from one thousand to ten thousand stabilizes an estimated tail probability. Keeping each simulated sample at thirty observations leaves the underlying sampling distribution unchanged. Increasing the observations inside each sample is a different operation and can reduce its spread.
A simulation models independent successes with probability 2/10 using digits 0–9 equally likely. Which mapping is valid?
- Count the digits in the proposed success set; endpoints are included.
- There are 2 success digits among ten equally likely digits.
- Why an alternative fails: Count an inclusive range incorrectly, assigning one extra digit to success.
Compare the other answer choices
Count an inclusive range incorrectly, assigning one extra digit to success.
Use one success digit regardless of the requested probability.
Assign every digit to success and eliminate failures, rather than using the stated chance.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which operation preserved the relationship and why the result makes sense.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
AP Statistics Course and Exam Description, effective Fall 2026