Probability
Conditional Probability
Grade 12
Question:
<p>In a certain town, 40% of the people have brown hair, 25% have brown eyes, and 15% have both brown hair and brown eyes. If a person selected at random from the town has brown hair, the probability that he also has brown eyes is</p>
<p>(1) 1/5</p>
<p>(2) 3/8</p>
<p>(3) 1/3</p>
<p>(4) 2/3</p>
Step-by-Step Solution
Key Concept: Use the definition of conditional probability: P(Brown Eyes | Brown Hair) = P(Both) / P(Brown Hair). The condition 'has brown hair' restricts the sample space, so we only consider the subset of brown-haired people.
<p><strong>Step 1:</strong> Identify the given information.</p><p>P(Brown Hair) = 0.40</p><p>P(Brown Eyes) = 0.25</p><p>P(Brown Hair AND Brown Eyes) = 0.15</p><p><strong>Step 2:</strong> Apply the conditional probability formula.</p><p>We need P(Brown Eyes | Brown Hair) = P(Brown Hair ∩ Brown Eyes) / P(Brown Hair)</p><p><strong>Step 3:</strong> Substitute values.</p><p>P(Brown Eyes | Brown Hair) = 0.15 / 0.40 = 15/40 = 3/8</p><p><strong>Step 4:</strong> Simplify.</p><p>3/8 = 0.375 or 37.5%</p><p>∴ Answer: B (which is 3/8 or 0.375)</p>
Correct Answer: B