<p>A three-digit number is selected at random from the set of all three-digit numbers. The probability that the number selected has all the three digits same is</p>
Step-by-Step Solution
Key Concept: Count three-digit numbers with all digits same (111, 222, ..., 999) and divide by total three-digit numbers (100-999). The constraint is that first digit cannot be 0, which affects the total count but not the favorable outcomes.
<p><strong>Step 1:</strong> Identify three-digit numbers with all digits same.</p><p>These are: 111, 222, 333, 444, 555, 666, 777, 888, 999</p><p>Favorable outcomes = 9</p><p><strong>Step 2:</strong> Count total three-digit numbers.</p><p>Three-digit numbers range from 100 to 999.</p><p>Total three-digit numbers = 999 - 100 + 1 = 900</p><p><strong>Step 3:</strong> Calculate probability.</p><p>P(all three digits same) = 9/900 = 1/100</p><p>∴ Answer: D (1/100 or 0.01)</p>
Correct Answer: D