Learning Resources
Lesson
In order to pass the driver's test, you need to answer 20 questions correctly on a multiple choice test that contains 25 items (this means you must score 80% on the test to pass). Since you already know you have answered15 correctly, you only need to answer 5 more correctly from the remaining 10 questions in order to pass. There are 5 choices for the answer to each question. However, you are making a random guess as to which of these is correct.
The problem facing you looks like this (ignore the other 15 questions as they are correct):
Quest # Choices
1 (a) (b) (c) (d) (e)
2 (a) (b) (c) (d) (e)
3 (a) (b) (c) (d) (e)
4 (a) (b) (c) (d) (e)
5 (a) (b) (c) (d) (e)
6 (a) (b) (c) (d) (e)
7 (a) (b) (c) (d) (e)
8 (a) (b) (c) (d) (e)
9 (a) (b) (c) (d) (e)
10 (a) (b) (c) (d) (e)
You make a random guess for each of the questions. What is the probability you will guess 5 correctly?
The Solution
Since we have not yet covered in this chapter the skills necessary to calculate this probability theoretically, you have to determine the probability experimentally. To do this you need to set up a simulation to model the situation.
The number of trials necessary almost dictates that some form of technology (calculator or spreadsheet) be used. One possibility is to use random numbers for each of the five choices (a) to (e). Let one of these numbers (say the number 5) designate a correct response and the other 4 numbers designate an incorrect response. Do 10 (for the 10 questions) trials of these random numbers and see if you "guessed correctly" on 5 of them.
The steps necessary to use the TI83 to do 10 such trials can be seen by clicking here.
This simulation would represent "guessing on one test". To determine the required probability you would have to run this simulation many times. Run it at least 50 times and record your answers in a table like the one shown below. The first row is already filled in using the numbers generated on the TI83 in the viewlet above.
| Trial# | q1 | q2 | q3 | q4 | q5 | q6 | q7 | q8 | q9 | q10 | pass? |
| 1 | 5 | 4 | 2 | 2 | 5 | 5 | 1 | 1 | 4 | 5 | no |
| 2 | |||||||||||
| 3 | |||||||||||
| 4 |
After at least 50 repetitions of the simulation calculate the probability by dividing the number of simulations which yielded a "pass" by the total number of simulations. Keep this answer for future reference as you will compare the experimental value you obtained here with the theoretical value you will find later in this unit.
Activity
Complete the part of the Chapter Project assigned on page 306 in your text.
Test Yourself
There are no extra questions for this lesson. Simply submit your work to date to your online teacher.