Results of guessing on a 5-question true-false test
The following are instructions for a collaborative activity to simulate the results of pure guessing on a 5-question true-false test.
Nadine did not read the assigned chapters in "Great Expectations" last night. Rather than beg the teacher for an extension, she decides to guess the answer for all of the answers on the in-class true-false test. Is this a wise decision? Let’s investigate by simulation. There are five questions on the test. Assume that 1 point is awarded for each right answer and 0 points is awarded for each wrong answer. The simulation needs to be designed to give an approximate distribution for the number of correct answers on such a test.
- Use the selection of a random number (or random outcome) to correspond to guessing for each true-false question. What is the probability of guessing the correct answer on any one question? Devise an event involving the selection of a random number that will result in this same probability.
- Each trial of the simulation should represent one taking of the test; therefore, each trial must include five random selections leading to question outcomes. Select five random numbers, with outcomes as defined above. Count the number of correct answers obtained. Record this number.
- Repeat the procedure for a total of 50 trials (which represents taking the test 50 times). Record the number of correct answers for each trial.
- Calculate the average number of questions answered correctly per trial. This is an approximation to Nadine's expected number of correct answers when she takes the test by guessing. Construct a plot of the results.
- Approximate the probability that you would get three or more correct answers by guessing.
Review the instructions with the full group, then form the students into teams of 2-3 students to carry out the activity. The students are free to use any of the following tools to generate the random numbers:
- table of random numbers
- spreadsheet program
- graphing calculator
- bag of marbles
Have the students come together in a group and discuss the following:
- method used to generate probabilities
- design of chart
- average number of questions answered correctly
- probability of scoring 3 or higher on the test by guessing alone.