1. **Stating the problem:** A bag contains 8 identical red balls and an unknown number of white balls, say $w$. The probability of drawing a red ball initially is given as $\frac{10}{18}$. After adding 4 more white balls, we want to find the new probability of drawing a red ball. 2. **Initial probability formula:** The probability of drawing a red ball initially is $$P(\text{red}) = \frac{\text{number of red balls}}{\text{total number of balls}} = \frac{8}{8 + w} = \frac{10}{18}$$ 3. **Solve for $w$:** Cross-multiply: $$8 \times 18 = 10 \times (8 + w)$$ $$144 = 80 + 10w$$ Subtract 80 from both sides: $$144 - 80 = 10w$$ $$64 = 10w$$ Divide both sides by 10: $$w = \frac{64}{10} = 6.4$$ 4. **After adding 4 white balls:** New number of white balls: $$w_{new} = 6.4 + 4 = 10.4$$ Total balls now: $$8 + 10.4 = 18.4$$ 5. **New probability of drawing a red ball:** $$P_{new}(\text{red}) = \frac{8}{18.4}$$ Simplify: $$P_{new}(\text{red}) = \frac{8}{18.4} \approx 0.4348$$ **Final answer:** The probability of drawing a red ball after adding 4 white balls is approximately $0.435$ or $\frac{8}{18.4}$.