There are
5 equally possible choices for each of the multiple choice questions on an exam and you guess on each of
8 multiple choice questions.
What is the probability that you will get at least half of them correct?
How many questions, out of
8 questions, do you have to get correct to get half or more correct?
The lower bound of half of
8 is
4.
Half or more of
8 is
4,
5,
6,
7, or
8 questions correct.
Less than half of
8 is
0,
1,
2, or
3 questions correct.
The lower bound of half or more of
n questions can be written in Excel as follows.
=INT((n / 2) - 0.5)
Here is a table showing the values of half or more of
n for some values of
n.
What is the probability that you get half or more questions correct.
The probability of guessing the answer correct from
5 choices is
1/5 =
0.20.
Here is the probability of passing.
If you can eliminate
1 choice from each of multiple choice question on an exam, what is the probability that you will get at least half of them correct?
The probability of guessing the answer correct from the remaining
4 choices is
1/4 =
0.25.
Here is the probability of passing.
If you can eliminate
2 choices from each of multiple choice question on an exam, what is the probability that you will get at least half of them correct?
The probability of guessing the answer correct from the remaining
3 choices is
1/3 ≈
0.33.
Here is the probability of passing.
If you can eliminate
3 choices from each of the multiple choice questions on an exam, what is the probability that you will get at least half of them correct?
The probability of guessing the answer correct from the remaining
2 choices is
1/2 =
0.50. Such questions are the same as True-False questions (i.e.,
2 choices for each question).
Here is the probability of passing.
If you can eliminate
4 choices from each of the multiple choice questions on an exam, what is the probability that you will get at least half of them correct?
The probability of guessing the answer correct from the remaining
1 choice is
1/1 =
1.00.
Here is the probability of passing.
Here are all of these ways.
In general, does it make sense to eliminate choices on multiple choice questions, even if you are otherwise guessing?
Here is a spreadsheet for the formulas, in general.
Here is a spreadsheet of the values for the above spreadsheet formulas.
(XLS omitted)
