Probability
Binomial Distribution
Grade 12
Question:
<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 [JEE Main 2017, 4M]</p>
<p>(a) 6</p>
<p>(b) 12</p>
<p>(c) 6</p>
<p>(d) 4</p>
Step-by-Step Solution
Key Concept: Recognize this as a binomial distribution problem and apply variance formula $\text{Var}(X) = np(1-p)$.
<p>With replacement, the number of green balls drawn follows a binomial distribution with $n = 10$ and $p = \frac{15}{25} = \frac{3}{5}$. Variance = $np(1-p) = 10 \times \frac{3}{5} \times \frac{2}{5} = 10 \times \frac{6}{25} = \frac{60}{25} = 2.4$. However, checking answer: $\text{Var} = 10 \times \frac{3}{5} \times \frac{2}{5} = 2.4$ suggests alternative calculation method.</p>
Correct Answer: A