<p>An integer is chosen at random and squared. Find the probability that the unit digit of the square is 1 or 5.</p>
Step-by-Step Solution
Key Concept: Analyze how unit digits behave under squaring: a number's unit digit depends only on its own unit digit. Check all 10 possible unit digits (0-9) and see which yield unit digit 1 or 5 when squared.
<p><strong>Step 1: Identify the pattern.</strong> When we square an integer, its unit digit depends only on the unit digit of the original integer. We need to check which unit digits (0, 1, 2, ..., 9) produce squares with unit digit 1 or 5.</p><p><strong>Step 2: Square each unit digit:</strong></p><p>0² = 0 (unit digit: 0)<br>1² = 1 (unit digit: 1) ✓<br>2² = 4 (unit digit: 4)<br>3² = 9 (unit digit: 9)<br>4² = 16 (unit digit: 6)<br>5² = 25 (unit digit: 5) ✓<br>6² = 36 (unit digit: 6)<br>7² = 49 (unit digit: 9)<br>8² = 64 (unit digit: 4)<br>9² = 81 (unit digit: 1) ✓</p><p><strong>Step 3: Count favorable outcomes.</strong> Unit digits that produce 1 or 5: {1, 5, 9}. That's 3 favorable outcomes out of 10 possible unit digits.</p><p><strong>Step 4: Calculate probability.</strong> Since each unit digit appears with equal frequency among all integers, P(unit digit of square is 1 or 5) = 3/10</p><p>∴ Answer: B (3/10)</p>
Correct Answer: B