<p>Dialing a telephone number an old man forgets the last two digits remembering only that these are different dialed at random. The probability that the number is dialed correctly is</p>
Step-by-Step Solution
Key Concept: The last two digits must be different and selected from 0-9. We need to count favorable outcomes (1 correct pair) divided by total outcomes (all possible pairs of different digits).
<p><strong>Step 1:</strong> Identify the sample space. The last two digits must be different and each is from {0,1,2,...,9}.</p><p><strong>Step 2:</strong> Count total possible ways to dial two different digits: First digit has 10 choices (0-9), second digit has 9 choices (any digit except the first). Total = 10 × 9 = 90</p><p><strong>Step 3:</strong> Count favorable outcomes. Only 1 way to dial the correct number (the specific correct pair of different digits).</p><p><strong>Step 4:</strong> Apply probability formula: P(correct) = Favorable outcomes / Total outcomes = 1/90</p><p>∴ Answer: B</p>
Correct Answer: B