Probability
Classical Definition of Probability
Grade 12
Question:
<p>Consider the following assignments of probabilities for outcomes of sample space \(S = \{1, 2, 3, 4, 5, 6, 7, 8\}\).</p><table border='1'><tr><th>Number (X)</th><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td></tr><tr><th>Probability P(X)</th><td>0.15</td><td>0.23</td><td>0.12</td><td>0.10</td><td>0.20</td><td>0.08</td><td>0.07</td><td>0.05</td></tr></table><p>Find the probability that <strong>(b)</strong> \(X\) is a number greater than 4.</p>
Step-by-Step Solution
Key Concept: Identify all outcomes in the sample space satisfying the condition X > 4, then sum their individual probabilities directly from the given probability distribution.
<p><strong>Step 1:</strong> Identify outcomes where X > 4</p><p>From sample space S = {1, 2, 3, 4, 5, 6, 7, 8}, the condition X > 4 gives us: X ∈ {5, 6, 7, 8}</p><p><strong>Step 2:</strong> Sum the probabilities of these outcomes</p><p>P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)</p><p>P(X > 4) = 0.20 + 0.08 + 0.07 + 0.05</p><p><strong>Step 3:</strong> Calculate the sum</p><p>P(X > 4) = 0.40</p><p>∴ Answer: <strong>0.4</strong></p>
Correct Answer: 0.4