Probability
Binomial Distribution
Grade 12
Question:
<p>A fair coin is tossed \(n\) times. If the variance of the number of heads is 2, then \(n =\) <em>[JEE Advanced 2016]</em></p>
Step-by-Step Solution
Key Concept: X ~ Bin(n, 1/2). Var(X) = n/4 = 2 \to n = 8.
<p>$X \sim \text{Bin}(n, \frac{1}{2})$.</p><p>$\text{Var}(X) = n \cdot \frac{1}{2} \cdot \frac{1}{2} = \frac{n}{4} = 2$.</p><p>$n = 8$.</p>
Correct Answer: 8