<p>In a single throw of two dice what is the probability of obtaining a number greater than 7, if 4 appears on the first dice?</p>
Step-by-Step Solution
Key Concept: This is conditional probability where we need P(sum > 7 | first die = 4). Given the first die shows 4, the second die must show 4, 5, or 6 to make the sum greater than 7.
<p><strong>Step 1:</strong> Identify the condition: First die = 4 (given).</p><p><strong>Step 2:</strong> Determine the restricted sample space. Since first die shows 4, possible outcomes are: (4,1), (4,2), (4,3), (4,4), (4,5), (4,6). Total outcomes = 6.</p><p><strong>Step 3:</strong> Find favorable outcomes where sum > 7. We need 4 + second die > 7, so second die > 3. Favorable outcomes: (4,4), (4,5), (4,6). Count = 3.</p><p><strong>Step 4:</strong> Apply conditional probability formula: P(sum > 7 | first die = 4) = Favorable outcomes / Total outcomes in restricted sample space = 3/6.</p><p><strong>∴ Answer: 1/2</strong></p>
Correct Answer: 1/2