This is my first post so please forgive me if I have posted this in the wrong forum or if this is simple and has already been answered somewhere already (I have searched and not found the solution).

Basically what I am trying to do is calculate the likelihood (percentage) of getting the correct (known) answer to a question if we have two people answer the same the question and then a third person if the first two disagree.

Example:

I have 10 people, each are asked a question with the following results:

Person 1 = Correct
Person 2 = Incorrect
Person 3 = Correct
Person 4 = Incorrect
Person 5 = Correct
Person 6 = Incorrect
Person 7 = Correct
Person 8 = Correct
Person 9 = Incorrect
Person 10 = Correct

So looking at possible combinations of answer we have:

Person 1 and 2 = Disagreement
Person 1 and 3 = Correct
Person 1 and 4 = Disagreement
Person 1 and 5 = Correct
Person 1 and 6 = Disagreement
Person 1 and 7 = Correct
Person 1 and 8 = Correct
Person 1 and 9 = Disagreement
Person 1 and 10 = Correct

Person 2 and 3 = Disagreement
Person 2 and 4 = Incorrect
Person 2 and 5 = Disagreement
Person 2 and 6 = Incorrect
Person 2 and 7 = Disagreement
Person 2 and 8 = Disagreement
Person 2 and 9 = Incorrect
Person 2 and 10 = Disagreement

Person 3 and 4 = Disagreement
Person 3 and 5 = Correct
Person 3 and 6 = Disagreement
Person 3 and 7 = Correct
Person 3 and 8 = Correct
Person 3 and 9 = Disagreement
Person 3 and 10 = Correct

……..and so on.

What I would like to do is calculate the percentage of correct answers, the percentage of incorrect answers…and….and this is where my brain starts to melt, the percentage of correct and incorrect results if we sent each combination which provided a disagreement to a third person and we took the majority answer e.g.

Person 1 and 2 = Disagreement

Person 1 = Correct, Person 2 = Incorrect, Person 3 = Correct so answer is Correct

Person 1 = Correct, Person 2 = Incorrect, Person 4 = Incorrect so answer is Incorrect

Person 1 = Correct, Person 2 = Incorrect, Person 5 = Correct so answer is Correct

…….and so on.

Is this something I can calculate in excel?

And help in this would be very much appreciated.


Regards

Simon