<p>A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is</p>
Step-by-Step Solution
Key Concept: When drawing with replacement, each draw is an independent Bernoulli trial with fixed probability p = 15/25 = 3/5. The number of green balls follows a binomial distribution B(n=10, p=3/5), so variance = np(1-p).
<p><strong>Step 1:</strong> Identify the distribution type. Since balls are drawn <strong>with replacement</strong>, each draw is independent with the same probability of drawing a green ball.</p><p><strong>Step 2:</strong> Calculate the probability of drawing a green ball: p = 15/(15+10) = 15/25 = 3/5</p><p><strong>Step 3:</strong> The number of green balls X in 10 draws follows a Binomial distribution: X ~ B(n=10, p=3/5)</p><p><strong>Step 4:</strong> For a binomial distribution, variance = np(1-p)</p><p><strong>Step 5:</strong> Calculate: Var(X) = 10 × (3/5) × (1 - 3/5) = 10 × (3/5) × (2/5) = 10 × 6/25 = 60/25 = <strong>12/5 or 2.4</strong></p><p>∴ Answer: D</p>
Correct Answer: D