1. **State the problem:** Aditi has 1 white sock and 9 yellow socks in a bag. She draws one sock, replaces it, then draws another sock. We need to find the probability that the two socks drawn are of different colors. 2. **Understand the problem:** Since the sock is replaced after the first draw, the draws are independent events. The total number of socks is $1 + 9 = 10$. 3. **Define events:** - Let $W$ be drawing a white sock. - Let $Y$ be drawing a yellow sock. 4. **Calculate individual probabilities:** - Probability of drawing white sock: $P(W) = \frac{1}{10}$ - Probability of drawing yellow sock: $P(Y) = \frac{9}{10}$ 5. **Find probability of two socks of different colors:** This can happen in two ways: - First sock white, second sock yellow: $P(W) \times P(Y) = \frac{1}{10} \times \frac{9}{10} = \frac{9}{100}$ - First sock yellow, second sock white: $P(Y) \times P(W) = \frac{9}{10} \times \frac{1}{10} = \frac{9}{100}$ 6. **Add these probabilities:** $$ P(\text{different colors}) = \frac{9}{100} + \frac{9}{100} = \frac{18}{100} $$ 7. **Simplify the fraction:** $$ \frac{18}{100} = \frac{\cancel{18}^{9}}{\cancel{100}^{50}} = \frac{9}{50} $$ **Final answer:** The probability that Aditi takes two socks of different colors is $\boxed{\frac{9}{50}}$.