<p>From \(\{1, 2, \ldots, 15\}\), one number selected randomly. \(P(\text{multiple of 3 or 5}) =\) <em>[JEE Advanced 2018]</em></p>
Step-by-Step Solution
Key Concept: Multiples of 3: {3,6,9,12,15}=5 numbers. Multiples of 5: {5,10,15}=3. Multiples of 15: {15}=1. By inclusion-exclusion: 5+3-1=7.
<p>Multiples of 3 in $\{1,\ldots,15\}$: $\{3,6,9,12,15\}$ \to 5 numbers.</p><p>Multiples of 5: $\{5,10,15\}$ \to 3 numbers.</p><p>Multiples of 15: $\{15\}$ \to 1 number.</p><p>By inclusion-exclusion: $5+3-1=7$.</p><p>$P = \dfrac{7}{15}$</p>
Correct Answer: B