An instructor has a question bank consisting of 200 easy True / False questions, 300 difficult True / False questions, 400 easy multiple-choice questions and 500 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?

Let us denote E = easy questions, M = multiple choice question, D = difficult questions and T = true/false questions. Total number of questions = 1400 Total number of multiple-choice questions = 900 Probability of selecting easy multiple-choice question is P ( E ∩ M) = 400/1400 = 2/7 Probability of selecting multiple is P ( M) = 900/1400 = 9/14 P(E|M) represents the probability that a randomly selected question will be an easy question, given that is a multiple-choice question.  Therefore, P(E|M) = P( E ∩ M)/P(M) = (2/7)/(9/14) = 4/9 Therefore, required probability = 4/9