Probability
Conditional Probability
Grade 12
Question:
<p>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 test bank, what is the probability that it will be an easy question given that it is a multiple choice question?</p>
<p>(a) \(\frac{1}{9}\)</p>
<p>(b) \(\frac{2}{9}\)</p>
<p>(c) \(\frac{4}{9}\)</p>
<p>(d) \(\frac{5}{9}\)</p>
Step-by-Step Solution
Key Concept: Conditional probability: restrict the sample space to multiple choice questions only, then find the proportion that are easy.
<p><strong>Step 1:</strong> Total easy multiple choice questions: 500.</p><p><strong>Step 2:</strong> Total difficult multiple choice questions: 400.</p><p><strong>Step 3:</strong> Total multiple choice questions: $500 + 400 = 900$.</p><p><strong>Step 4:</strong> $P(\text{easy | multiple choice}) = \frac{\text{Number of easy MC questions}}{\text{Total MC questions}} = \frac{500}{900} = \frac{5}{9}$.</p>
Correct Answer: D