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 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?

Answer 1

The given data can be tabulated as

	True/False	Multiple choice	Total
Easy	300	500	800
Difficult	200	400	600
Total	500	900	1400

Total number of questions = 300 + 200 + 500 + 400 = 1400

Let us denote easy and multiple-choice questions by E and F respectively, and then

n(E) = 300 + 500 = 800

n(F) = 500 + 400 = 900

E ∩ F: 'Easy Multiple Choice Questions' i.e. n(E ∩ F) = 500

or  P(E ∩ F) = `500/1400`

and P(F) = `900/1400`

Hence,`P(E/F) = (P(E ∩ F))/(P(F))`

`= (500/1400) ÷ (900/1400)`

= `5/9`