Probability of Getting 40/40 on MCQ Test by Guessing

  • Thread starter Thread starter mohdakram
  • Start date Start date
  • Tags Tags
    Probability
AI Thread Summary
The probability of getting a perfect score of 40/40 on an MCQ test by guessing is calculated as (1/4)^40, which is the correct method. The alternative approach using combinations, 1/(160C40), is incorrect because it assumes multiple answers can be selected for a single question. For the scenario where a student is confident about 30 questions and must guess on 10, the probability of scoring above 30 is determined by the likelihood of missing all guessed questions. Since there are no penalties for wrong answers, the only way to score below 30 is to fail all guesses. Thus, the focus is on calculating the probability of missing all guessed questions.
mohdakram
Messages
10
Reaction score
0

Homework Statement



This question isn't in a book, but I want to know the answer for myself.

Q. If I take an MCQ test with 40 questions, each question has 4 possible answers with only one being correct, what is the probability of getting 40/40 in the test by guessing?

I've tried solving this by doing (1/4)^40, but then I thought of doing 1/(160C40) and I got different answers. Why is that so and which is the correct way.

Q. If I am sure of 30 questions and unsure about 10 (have to guess them), what is the probability of getting above 30 in the test.(I don't lose marks for wrong answers)
 
Physics news on Phys.org
mohdakram said:

Homework Statement



This question isn't in a book, but I want to know the answer for myself.

Q. If I take an MCQ test with 40 questions, each question has 4 possible answers with only one being correct, what is the probability of getting 40/40 in the test by guessing?

I've tried solving this by doing (1/4)^40, but then I thought of doing 1/(160C40) and I got different answers. Why is that so and which is the correct way.

Q. If I am sure of 30 questions and unsure about 10 (have to guess them), what is the probability of getting above 30 in the test.(I don't lose marks for wrong answers)
For the first question, (1/4)^40 is correct. Your other answer involving C(160,40) seems to assume you can select more than one answer to a single question.

For the second question, your score will be above 30 unless you miss all 10 questions you guess at. What's the probability of that?
 
Last edited:

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
View full post »

Similar threads

What is the ideal number of guesses to maximize your marks in MCQs?
Replies
29
Views
3K
Probability of Receiving 2-4-6-7-Queen-King Sequence from 40 Cards
Replies
2
Views
1K
How much would you pay to play this fair coin flipping game?
Replies
29
Views
6K
Solve Word Problem: 30 Persons in 4 Days = 40 Persons in x Days
Replies
6
Views
2K
Where is my logic wrong (lottery problem)
Replies
7
Views
2K
What is the Probability of Passing a Test by Randomly Guessing?
Replies
2
Views
2K
Probability of No Mixed-Sex Rooms with 40 Randomly Assigned People
Replies
12
Views
2K
Probability using combinations or alternatives
Replies
12
Views
2K
Question on Probability - been way too long since college
Replies
12
Views
2K
Probabilities on a spinner
Replies
3
Views
191

Hot Threads

Recent Insights

Back
Top