Question

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 from the test question bank, what is the probability that it will be an easy question given that it is a multiple choice question?

Answer 1

Describe the events as follows

E: ‘getting an easy question.’

F: ‘getting a multiple choice question.’

Total Questions = 300 + 200 + 500 + 400 = 1400

n(F) = 500 + 400 = 900, n(E ∩ F) = 500

\(P(F) = \frac{900}{1400} = \frac{9}{14},\) P(E ∩ F) = \(\frac{500}{1400}\) = \(\frac{5}{14}\)

Therefore the required probability

P(E/F) = \(\frac{P(E \cap F)}{P(F)} = \frac{\frac{5}{14}}{\frac{9}{14}} = \frac{5}{9}\).