A probability problem by REJOY mathew
In an entrance examination with multiple choice questions, with each question having four options and a single correct answer, suppose that only 20% candidates think they know the answer to one difficult question and only half of them know it correctly and the other half get it wrong. The remaining candidates pick one option out of the four randomly and tick the same. If a candidate has correctly answered the question, what is the (conditional) probability that she knew the answer?
The answer is 0.33.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
The probability of getting the question correct is .1 1 + .1 0 + .8 .25 = .3. The probability the student knew the answer given the fact that he answered correctly is (probability of knowing the answer and getting it correct) / (probability of getting it correct) = .1 1 / .3 = .33333