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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?
Solution
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`
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