<p>Two dice are thrown. What is the probability that the sum of the numbers appearing on the two dices is 11, if 5 appears on the first?</p>
Step-by-Step Solution
Key Concept: Use conditional probability: Given that 5 appears on the first die, we need P(sum = 11 | first die = 5). Since the first die is fixed at 5, the second die must show 6 to get sum = 11, making this a simple counting problem rather than standard probability.
<p><strong>Step 1:</strong> Identify the condition: The first die shows 5 (this is given/fixed).</p><p><strong>Step 2:</strong> For the sum to be 11 when the first die is 5, we need: 5 + (second die) = 11, so the second die must show 6.</p><p><strong>Step 3:</strong> Since the first die is already determined to be 5, the sample space consists only of the possible outcomes of the second die: {1, 2, 3, 4, 5, 6}. This gives us 6 possible outcomes.</p><p><strong>Step 4:</strong> Favorable outcome: second die shows 6 (only 1 outcome).</p><p><strong>Step 5:</strong> P(sum = 11 | first die = 5) = Number of favorable outcomes / Total possible outcomes = 1/6</p><p>∴ Answer: A (1/6)</p>
Correct Answer: A