<p>In binomial distribution mean = <em>np</em> = 2 and variance <em>npq</em> = 1. Then find <em>P</em>(<em>x</em> ≥ 1).</p>
Step-by-Step Solution
Key Concept: From mean = np = 2 and variance = npq = 1, find p and q by dividing variance by mean to get q, then use binomial probability formula P(X ≥ 1) = 1 - P(X = 0).
<p><strong>Step 1:</strong> Find q using the given conditions.</p><p>Given: np = 2 and npq = 1</p><p>Dividing: npq/np = 1/2 → q = 1/2</p><p><strong>Step 2:</strong> Find p and n.</p><p>Since q = 1/2, we have p = 1 - q = 1/2</p><p>From np = 2: n(1/2) = 2 → n = 4</p><p><strong>Step 3:</strong> Calculate P(X ≥ 1) using complement.</p><p>P(X ≥ 1) = 1 - P(X = 0)</p><p>P(X = 0) = C(4,0)(1/2)⁰(1/2)⁴ = 1 · 1 · 1/16 = 1/16</p><p><strong>Step 4:</strong> Final answer.</p><p>P(X ≥ 1) = 1 - 1/16 = 15/16</p><p>∴ Answer: B</p>
Correct Answer: B