<p>A class consists of 80 students, 25 of them are girls and 55 are boys. If 10 of them are rich and the remaining are poor and also 20 of them are intelligent, then the probability of selecting an intelligent rich girl is</p>
Step-by-Step Solution
Key Concept: When no overlap information is given between independent categorical attributes (gender, wealth, intelligence), assume independence and multiply individual probabilities. The probability of selecting a student with all three specific properties equals P(girl) × P(rich) × P(intelligent).
<p><strong>Step 1:</strong> Identify the given information.</p><p>Total students = 80</p><p>Girls = 25, so P(Girl) = 25/80 = 5/16</p><p>Rich = 10, so P(Rich) = 10/80 = 1/8</p><p>Intelligent = 20, so P(Intelligent) = 20/80 = 1/4</p><p><strong>Step 2:</strong> Since no information about overlap between categories is provided, we assume these attributes are independent.</p><p><strong>Step 3:</strong> Apply the multiplication rule for independent events.</p><p>P(Intelligent AND Rich AND Girl) = P(Girl) × P(Rich) × P(Intelligent)</p><p>= (5/16) × (1/8) × (1/4)</p><p>= 5/512</p><p>∴ Answer: C</p>
Correct Answer: C