Chances of 8 of 24 guesses test on 4-choice exam being correct

[marvingrayson333]

What are the chances of getting 8 questions correct on a 24-question exam where each question has 4 choices?

Can someone walk me through how I would do this problem? Once I have a sense of how to do it with this one, I'll be able to do it on my own. I just need the formula for how I would do it and use it as an example for further questions.

 

[Deleted member 4993]

What are the chances of getting 8 questions correct on a 24-question exam where each question has 4 choices?

Can someone walk me through how I would do this problem? Once I have a sense of how to do it with this one, I'll be able to do it on my own. I just need the formula for how I would do it and use it as an example for further questions.

Please follow the rules of posting in this forum, enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-462270

Please share your work/thoughts with us - so that we know where to begin to help you.

If you have no clue -

Start with:

For 1 problem, what are the chances of getting it correct?

For 1 problem, what are the chances of getting it wrong?

continue.....

 

[JeffM]

Is the question relating to guessing correctly at least 8 questions or exactly 8 questions?

Are the guesses completely random?

This is why we ask you to copy each question completely and exactly?

Do you need a hint to get started or have you hit a roadblock in your work. If the latter, we need to see that work.

 

[Dr.Peterson]

What are the chances of getting 8 questions correct on a 24-question exam where each question has 4 choices?

Can someone walk me through how I would do this problem? Once I have a sense of how to do it with this one, I'll be able to do it on my own. I just need the formula for how I would do it and use it as an example for further questions.

Let's suppose that the question is really this:

What is the probability that a student will get exactly 8 of 24 questions on a multiple-choice exam correct, if he guesses randomly and there are 4 choices for each question?​

My first question to you will be, have you learned about the binomial distribution? If not, I'd ask what you know about combinations, and about probabilities of independent events.

This illustrates why we ask not only for an exact copy of the entire problem, and your work as far as you can get, but also for the context of the question (such as what you have learned in your course, and what the current topic is).

 

[marvingrayson333]

Please follow the rules of posting in this forum, enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-462270

Please share your work/thoughts with us - so that we know where to begin to help you.

If you have no clue -

Start with:

For 1 problem, what are the chances of getting it correct?

For 1 problem, what are the chances of getting it wrong?

continue.....

Let me rephrase it:

What will be the answer if a multiple choice test consisting of 24 questions with four choices each, and the student guesses the answer to each question? What is the probability that he gets 8 questions correctly?

 

[Deleted member 4993]

Let me rephrase it:

What will be the answer if a multiple choice test consisting of 24 questions with four choices each, and the student guesses the answer to each question? What is the probability that he gets 8 questions correctly?

Please post the EXACT problem as it was presented to you. Please do not rephrase or paraphrase it. In these problems - every word may carry specific constraints. We suspect the exact problem statement will clarify whether:

1) Exactly 8 problems are correct or

2) At least 8 problems are correct.

Please read the responses above for need of further clarification.

Please share your thoughts/work so that we can now where to begin to help you

 

[Dr.Peterson]

Let me rephrase it:

What will be the answer if a multiple choice test consisting of 24 questions with four choices each, and the student guesses the answer to each question? What is the probability that he gets 8 questions correctly?

Also, please answer my questions about context. We will explain things differently depending on whether you have learned about the binomial distribution, or the normal approximation to the binomial distribution, or neither, and also depending on whether the problem explicitly or implicitly indicates exactly 8, at least 8, or no more than 8 correct.