Calculating Expected Value: A Multiple Choice Quiz Question

In summary, the conversation discussed the calculation of expected value for a multiple choice test with 6 answers, where one is correct and the rest are wrong. The question was how many points should be subtracted for a wrong answer so that the average score for randomly guessing is 0. The solution involved using a variable for the negative points and modifying the formula for expected value. The conversation also touched on the Texas Department of Education's Trilingual English/Spanish/Ebonics Program.
  • #1
ParisSpart
129
0
A question on a multiple choice test has 6 answers which just one is right and the other wrong.

If the amount of the correct answer is 10 points how many points should be substracted for a wrong answer so if nobody answers randomly choosing one of the 6 answers get, on average, 0 points?


I am trying to find the expected value like this : E(X)=10*P(X=10)+0*P(X=0) but the quiz doesn't take it correct where i am wrong?
 
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  • #2
That is the expected value if wrong answers do not give negative points.
The answer to the problem is not an expectation value, but the amount of negative points the wrong answers should get.
 
  • #3
and how i can fo this?
 
  • #4
What is "fo"?

Use some variable for the amount of negative points, and modify your formula for the expectation value accordingly. What do you know about this expectation value (given in the problem statement)?
 
  • #5
i will not use expected value?
 
  • #6
mfb said:
What is "fo"?

According to the Texas Department of Education Trilingual English/Spanish/Ebonics Program, "two 'n' dos be fo".
 
  • #7
You want the expected number of points for a response to be zero:

If you answer correctly , you get 10 points, like you said. If ( I'm assumming) you are

answering randomly, what is your probability of guessing correctly? What is your

probability of guessing incorrectly , if you guess at random?

You have the right set up, just follow-up on it.
 
  • #8
ParisSpart said:
A question on a multiple choice test has 6 answers which just one is right and the other wrong.

If the amount of the correct answer is 10 points how many points should be substracted for a wrong answer so if nobody answers randomly choosing one of the 6 answers get, on average, 0 points?I am trying to find the expected value like this : E(X)=10*P(X=10)+0*P(X=0) but the quiz doesn't take it correct where i am wrong?
This is unacceptable for homework, you've done this repeatedly. Going forward, you must use the homework template or your posts will be deleted.
 
  • #9
tadchem said:
According to the Texas Department of Education Trilingual English/Spanish/Ebonics Program, "two 'n' dos be fo".
LOL !

I think that be f0 .
 

1. What is Expected Value?

Expected Value is a statistical concept that represents the average value an outcome can be expected to have over time. It is calculated by multiplying each possible outcome by its probability and adding all of these values together.

2. How do you calculate Expected Value?

To calculate Expected Value, you must first determine the possible outcomes and their corresponding probabilities. Then, multiply each outcome by its probability and add all of these values together to get the Expected Value. The formula for Expected Value is: E(X) = Σ(x * p(x)), where E(X) is the Expected Value, x is the outcome, and p(x) is the probability of that outcome.

3. What is the significance of Expected Value?

Expected Value is important because it helps to make informed decisions based on probability. It can be used in various fields such as finance, economics, and gaming to determine the potential outcome of a situation and assess risk.

4. Can Expected Value be negative?

Yes, Expected Value can be negative. This indicates that the potential outcome of a situation is unfavorable or carries a risk of loss. However, a negative Expected Value does not guarantee a loss, as there is still a chance for a positive outcome.

5. How is Expected Value used in a multiple choice quiz?

In a multiple choice quiz, Expected Value is used to determine the most likely outcome for a random guess. Each answer choice is assigned a probability based on the number of options. The Expected Value can help the quiz taker to strategize and choose the most probable answer for a higher chance of success.

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