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

• mr_coffee
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.

#### mr_coffee

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.

ANy ideas?

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.

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.