True/false exam, they got 5/16 but i got 1/4, probability

In summary, the conversation discusses the question of how to pass a true/false quiz consisting of four questions worth 25% each by randomly guessing. The total number of possible outcomes is 16, and in order to pass, at least 3 out of 4 answers must be correct. The individual breaks the problem down using combinations but forgets to include the case where all 4 answers are correct, resulting in an incorrect answer of 4/16. The correct answer is 5/16, taking into account the additional case.
  • #1
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Ello ello!

I'm not sure how they are getting 5/16 as the answer.

The question is:
Suppose you take a true/false quiz consisting of four questions, each worth 25%. If a score of 50% or less fails the quiz, what is the probabillity that you can pass the quiz by randomly guessing each answer?

Well here is how I broke it down...
If you get a 50% or less you fail, so you need at least 3 out of the 4 right to get a 75%.

I then thought, how many possible outcomes are there? Well its like tossing a coin, its either Head or Tails or in this case True or False so you have:
2^4 = 16 possible outcomes.

Now I thought to use combinations, you want 4 choose 3,

Step 1: Choose first question (T or F)
Step 2: Choose 2nd question (T or F)
Step 3: choose 3rd qustion (T or F)
Step 4: choose 4th question (T or F)

but I soon realized I dont' think i can apply the multiplication rule on this, there are too many cases so i tried combinations and i said:

4 choose 3 = 4. So the probabily i said was:
4/16 = 1/4.

But the answer is 5/16.

ANy ideas?
 
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  • #2
Looks fine, but you forgot the case where you get all 4 answers right. There is only one case when this happens (4 choose 4 if you want to think of it that way) thus you will get one more and so the probability will be 5/16.
 
  • #3
wewt, I forgot all about that, thanks again! I'll send you money via pay pal :P
 

1. What is the probability of getting a correct answer on a true/false exam?

The probability of getting a correct answer on a true/false exam is 50% or 1/2. This is because there are only two possible options for each question: true or false.

2. How many questions do I need to answer correctly to get a passing grade on a true/false exam?

In order to get a passing grade on a true/false exam, you need to answer at least 8 out of 16 questions correctly. This means you need to have a score of 50% or higher.

3. If I only got 1 out of 4 questions correct, what is my overall percentage score?

Your overall percentage score on the true/false exam would be 25%. This is because you only answered 1 out of 4 questions correctly, which is equivalent to 25% of the total questions.

4. Is it possible to get a lower score on a true/false exam than someone who answered more questions correctly?

Yes, it is possible to get a lower score on a true/false exam if you answered fewer questions correctly. This is because the score is based on the percentage of questions answered correctly, not the total number of correct answers.

5. Can the probability of getting a correct answer on a true/false exam change?

No, the probability of getting a correct answer on a true/false exam remains constant at 50%. This is because each question has only two possible outcomes and the probability of each outcome remains the same for every question.

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