How to calculate the best way to fill out this test?

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In summary: If you leave one blank, you need 9 correct answers from 24, with expected 4.5 - this gives a ~.2% chance to pass. So the probability to pass is 10x higher if you guess all of them.In summary, when answering 25 multiple choice questions with 5 choices per question, there are three strategies to consider: maximizing expected points, maximizing probability of getting 100%, and maximizing probability of getting a passing score. The first strategy suggests answering as soon as you can eliminate one answer, the second strategy suggests filling in all answers, and the third strategy suggests guessing all answers. Leaving a question blank is only beneficial in the first strategy, where it yields the same expected points as eliminating one
  • #1
Head_Unit
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25 questions, multiple choice, 5 choices per question.
Correct = 6 points
blank = 1.5 points
wrong = 0 points.

I should know how to do this, but have a cold and simply can't wrap my head around it…

Danke Schoen!
 
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  • #2
Depends on your target.
If you want to maximize the expected points, answer as soon as you can exclude 1 answer (then you get on average (0+0+0+6)/4=1.5 points, the same as leaving it blank).
If you want to maximize the probability of getting 100%, fill in everything (just as an example that there can be different strategies for different targets).
 
  • #3
I think this is what you are looking for.
Working out the probable expectation points for the rest of the possible situations...

Looks like if you can identify and eliminate 1 or more answers as incorrect,
guessing among those remaining is as good or better than leaving it blank.

6 points for correct
same as guessing among 1 when all 4 wrong answers are eliminated

3 points for guessing among 2
1/2 x 6 = 3
this is guessing after eliminating 3 of the answers

2 points for guessing among 3
1/3 x 6 = 2
this is guessing after eliminating 2 of the answers

1.5 points for guessing among 4
1/4 x 6 = 1.5
this is guessing after eliminating 1 of the answers

1.5 points for leaving blank

1.2 points for guessing among 5
1/5 x 6 = 1.2
this is guessing without eliminating any answers

0 points for wrong
Get well soon...

edit... mfb, I'm unclear on the "...maximize the probability of getting 100%, fill in everything..." strategy. Leaving it blank is 1.5 points, but guessing without elimination is 1.2 points.
 
  • #4
bahamagreen said:
edit... mfb, I'm unclear on the "...maximize the probability of getting 100%, fill in everything..." strategy. Leaving it blank is 1.5 points, but guessing without elimination is 1.2 points.
If you leave one blank, you cannot reach 100% any more.

In the same way, to optimize the probability to get at least 25%, don't fill in anything.
 
  • #5
I'm was feeling a conflict between the strategy for making the highest possible score and the one you suggest for the best chance to make 100%... I think you are right, but it didn't feel right. :)

If you know the answer to 24 of 25, then you might justify "going for it" and guessing that one rather than leaving it blank. But the fewer you know you have right, the less likely this would work. The extreme case of going in clueless and not knowing any of the answers would require one to guess correctly all 25 times.

I think that would be p=(1/5)^25 or 1 out of almost 300 quadrillion.

I'm thinking that if you graphed both strategies (probability of scoring 100% over number of answers not known) that the max score strategy will start at 0% and remain flat because of choosing a blank over a total guess. The no-blanks strategy starts at .2 with one unknown answer, and approaches (1/5)^25 with subsequent unknown answers. So you are correct.

But, if you plot probable scores rather than probability of 100%, the max score strategy starts off at .25 and remains flat at .25, but the no-blanks method starts at .2 and fall fast.

If I did this is right (?), I'm surprised you are correct. I would not have seen it that way, Thanks.
 
  • #6
bahamagreen said:
If you know the answer to 24 of 25, then you might justify "going for it" and guessing that one rather than leaving it blank. But the fewer you know you have right, the less likely this would work. The extreme case of going in clueless and not knowing any of the answers would require one to guess correctly all 25 times.
If you just have "get 100% or fail", guessing all is still the best option, because leaving a question blank gives you a probability of zero.

To make a more realistic example: If the test is "get at least 40% or fail" and you have no idea about the answers, guessing all should be the best strategy (and it is clear that guessing some answers is necessary). You need 10 correct answers, with expected 5 - this gives a ~2% chance to pass.
 

1. How do I determine the best way to fill out the test?

The best way to fill out a test often depends on the specific test and your individual strengths and weaknesses. However, a good general strategy is to start with the questions you are most confident about and work your way through the test systematically. This can help build momentum and confidence as you progress through the test.

2. Should I skip difficult questions or come back to them later?

It is generally recommended to skip difficult questions and come back to them later if you have time. This can prevent you from getting stuck on one question and running out of time for the rest of the test. However, if a question is worth a significant amount of points, it may be worth spending extra time on it.

3. How do I manage my time effectively while taking the test?

Time management is key when taking a test. It is important to read and understand the instructions carefully before starting, and then pace yourself accordingly. If the test is timed, make sure to keep an eye on the clock and budget your time accordingly. Be sure to leave some time at the end to review and double-check your answers.

4. What is the best way to prepare for a test?

The best way to prepare for a test is to study and review the material in depth. This can include using study guides, flashcards, practice tests, and other resources. It is also important to get a good night's sleep before the test and eat a nutritious breakfast to fuel your brain.

5. How can I reduce test anxiety and stay calm during the test?

Test anxiety is a common issue for many people. To reduce it, try deep breathing exercises or other relaxation techniques before and during the test. It can also be helpful to remind yourself that you have prepared and are capable of doing well. Stay positive and focused, and take breaks if needed.

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