<p>A composite number is selected at random from the first 30 natural numbers and it is divided by 5. The probability that there will be a remainder is</p>
Step-by-Step Solution
Key Concept: Identify all composite numbers in 1-30, then determine which are divisible by 5 (remainder = 0). The probability of remainder requires counting composites NOT divisible by 5.
<p><strong>Step 1: List all composite numbers from 1 to 30.</strong></p><p>Composite numbers: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30</p><p>Total composite numbers = 19</p><p><strong>Step 2: Identify composites divisible by 5 (remainder = 0).</strong></p><p>Composites divisible by 5: 10, 15, 20, 25, 30</p><p>Count = 5</p><p><strong>Step 3: Find composites with remainder when divided by 5.</strong></p><p>Composites with remainder = 19 - 5 = 14</p><p><strong>Step 4: Calculate probability.</strong></p><p>P(remainder) = 14/19</p><p>∴ Answer: A</p>
Correct Answer: A