Question 1096375: On a multiple choice question with five choices, 70% of students know the correct answer and there is 5%
chance that a student will pick the wrong answer even if he knows it. If a student gets the problem right,
what is the probability that he really knows the answer?
Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!
The problem is not completely defined; we have to read between the lines to guess how to find an answer.
Suppose there are 1000 students. Then 700 know the answer, and 300 do not.
Of the 700 who know the right answer, 5% mark the wrong answer. (Oh, the number of times I have done that!). That means 35 who know the right answer mark the wrong answer; so there are 665 students who know the answer and mark it correctly.
Now the problem says nothing about the 300 students who don't know the right answer. So the only way to get an answer to the problem is to assume that with 5 answer choices 1/5 of those students will guess the right answer. So there are 60 students who get the right answer by guessing.
So now there are 665+60 = 725 students with the right answer; and 665 of those knew the answer.
So if a student gets the right answer, the probability that he knew the answer is 665/725 = 133/145.
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