An instructor has a question bank consisting of 300 easy True/Fal… - Vidyadip

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?

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Answer

Let E: it is an easy question
F: it is a multiple choice question.
Total number of questions = 300 + 200 + 500 + 400 = 1400
$P(E\cap F)=\frac{500}{1400}$ and P(F) = $\frac{500+400}{1400}=\frac{9}{14} $
Hence, required probability = $ P\left( {\frac{E}{F}} \right)$ =$\frac{P(E\cap F)}{P(F)}=\frac{5/14}{9/14}=\frac{5}{9}$

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