If A and B are events such that P(A|B) = P(B|A), then
Given: P(A|B) = P(B|A) ……….(i)
Now, we know that
By definition of conditional probability,
Using (i), we have
P(A|B) = P(B|A)
⇒ P(A) = P(B)
An instructor has a question bank consisting of 300 easy True / False questions, 200 difficult True / False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question?