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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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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Solution: total no of question = 1400

p (a) = \frac{300 + 500}{1400} = \frac{800}{1400}

p (b) = \frac{500 + 400}{1400} = \frac{900}{1400}

p (a \cap b) = \frac{500}{1400}

p (a ∣ b) = \frac{p ( a \cap b )}{p ( b )}

= \frac{\frac{500}{1400}}{\frac{900}{1400}}

= \frac{5}{9}

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Question Text	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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Text solutionVerified

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