Question

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

Answer 1

Number of easy True/False questions = 300
Number of difficult True/False questions = 200
Number of easy multiple choice questions = 500
Number of difficult multiple choice questions = 400

Total number of all such questions = n(S) = 1400

Let,
E represents an easy question and F represents a multiple choice question.

\(∴n(E) = 300+500 = 800\) 

And \(n(F) = 500+400 = 900\)

\(P(F)=\frac {n(F)}{n(S)}\)

\(P(F) =\frac {900}{1400}\)

\(n(E∩F)=500\)

⇒\(P(E∩F)=\frac {n(E∩F)}{n(S)}\)

\(P(E∩F) =\frac {500}{1400}\)

\(P(E|F)=\frac {P(E∩F)}{P(F)}\)

\(P(E|F)=\frac {500/1400}{900/1400}\)

\(P(E|F)=\frac {500}{900}\)

\(P(E|F)=\frac {5}{9}\)