Binomial Probability: Guessing on an 8-Question Multiple-Choice Test

GeoGebra Commands & Parameters

1. LaTeX(steps) → counter
2. LaTeX("\text{Use the buttons below to return to the original problem or}\cr\text{randomly generate a similar practice problem.}") → RandomizationText
3. Corner(1) → A
4. Corner(3) → B
5. First(Xall, questions + 1) → Xused
6. Last(Xused, questions - needed + 1) → Xneeded
7. First(ProbAll, questions + 1) → ProbUsed
8. Last(ProbUsed, questions - needed + 1) → ProbNeeded
9. First(ProbFormAll, questions + 1) → ProbFormUsed
10. LaTeX("\text{Determine whether this is a binomial distribution.}") → text1
11. LaTeX("\text{Make a probability distribution table.}") → text3
12. TableText({Append[Text["X"], Xused], Append[Text["P(X) formula"], ProbFormUsed], Append[Text["P(X) value"], ProbUsed]}, "vc|_") → text5
13. LaTeX((("\text{Determine the minimum number of problems needed to get " * percent) * "% on the test.}")) → text6
14. TableText({Append[Text["X"], Xneeded], Append[Text["P(X) value"], ProbNeeded]}, "vc|_") → text10
15. LaTeX("\text{Is this probability empirical or theoretical?}") → text14
16. LaTeX("\text{This is a theoretical probability because it is not based on data or an experiment;}\cr\text{it is based purely on calculation.}") → text15
17. LaTeX((((((("\text{If there are " * questions) * " problems on the test, then each problem is worth}\cr\textcolor{#000099}{\frac{100}{") * questions) * "}=") * weight) * "\%}\text{ on the test.}")) → text7
18. LaTeX((("\text{Use the distribution table to calculate the probability of guessing " * listRight) * " answers}\cr\text{correctly. The relevant section is copied below for convenience.}")) → text9
19. LaTeX("\text{Move the slider to solve the problem.}") → text0
20. LaTeX((((((((("\textcolor{#000099}{P(\text{" * percent) * "% right by guessing among ") * choices) * " choices on ") * questions) * " problems}) \approx ") * Psafe) * "}")) → text12
21. LaTeX((((((("\text{The test has " * questions) * " problems.}\cr\text{There are ") * choices) * " answer choices for each problem.}\cr\text{You want a score of at least ") * percent) * "%.}")) → Problem
22. LaTeX((((((((((("\text{This is a binomial distribution because your answer to each problem will be}\cr\text{either correct or incorrect. In this case, }\textcolor{#000099}{n}\text{ is }\textcolor{#000099}{" * questions) * "}\text{ (the number of problems) and }\cr\text{the probability }\textcolor{#000099}{p}\text{ of success (guessing the correct answer) is }\textcolor{#000099}{\frac{1}{") * choices) * "}}\text{ or }\textcolor{#000099}{") * success) * "}\text{.}\cr\text{Therefore, the probability of failure, }\textcolor{#000099}{1 – p}\text{, is }\textcolor{#000099}{1 – ") * success) * "}\text{ or }\textcolor{#000099}{") * failure) * "}.")) → text2
23. LaTeX("\text{Recall that in a binomial experiment which consists of }\textcolor{#000099}{n}\text{ trials, the probability}\cr\text{that there will be }\textcolor{#000099}{r}\text{ successes is }\textcolor{#000099}{P(r) = {_n}C_r p^r (1 – p)^{n – r}}\text{, where }\textcolor{#000099}{p}\text{ is the probability}\cr\text{of success. Use this formula to find each probability.}") → text4
24. LaTeX((((((((((((((("\text{If you want to score " * percent) * "%, then you need to get at least }\textcolor{#000099}{\frac{") * percent) * "}{") * weight) * "}}\text{ problems}\cr\text{right. Since each question is either entirely wrong or entirely right, fractional values}\cr\text{need to be rounded up. In this case, you need to get at least ") * needed) * " problems}\cr\text{right in order to get ") * percent) * "% on the test (") * needed) * " problems gives a score of ") * neededGives) * "%).}")) → text8
25. LaTeX((((("\text{Add the probabilites for guessing " * listRight) * " answers correctly to get}\cr\text{the probability of scoring ") * percent) * "% on this test by random guessing.}")) → text11
26. LaTeX((((((((("\text{The probability of getting a grade above " * percent) * "% on a test that has ") * choices) * " choices }\cr\text{for each of ") * questions) * " problems by guessing at every answer is about ") * PsafePercent) * "% (to two}\cr\text{decimal places).}")) → text13