1. **State the problem:** We need to find the probability that a randomly drawn ball from 25 balls numbered 1 to 25 is either even or a multiple of 8. 2. **Formula for probability:** $$\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$$ 3. **Identify favorable outcomes:** - Even numbers between 1 and 25: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24 (12 numbers) - Multiples of 8 between 1 and 25: 8, 16, 24 (3 numbers) 4. **Use the formula for union of two events:** $$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$ where - $A$ = event "number is even" - $B$ = event "number is multiple of 8" 5. **Calculate counts:** - $|A| = 12$ - $|B| = 3$ - $|A \cap B|$ = numbers that are both even and multiples of 8 = multiples of 8 (since all multiples of 8 are even) = 3 6. **Calculate number of favorable outcomes:** $$|A \cup B| = |A| + |B| - |A \cap B| = 12 + 3 - 3 = 12$$ 7. **Calculate probability:** $$P = \frac{12}{25} = 0.48$$ **Final answer:** The probability that the number drawn is even or a multiple of 8 is **0.48**.