1. **Problem statement:** We have 8 cards numbered 1 to 8. Two cards are drawn successively with replacement. We want to find the probability that the absolute difference between the two numbers drawn is equal to 3. 2. **Understanding the problem:** Since the draws are with replacement, the total number of possible outcomes is $8 \times 8 = 64$. 3. **Finding favorable outcomes:** Let the first card drawn be $x$. The second card drawn must be either $x+3$ or $x-3$ to have an absolute difference of 3. 4. **Counting valid pairs:** - For $x=1$, second card can be $4$ (valid) - For $x=2$, second card can be $5$ (valid) - For $x=3$, second card can be $6$ (valid) - For $x=4$, second card can be $1$ or $7$ (2 valid) - For $x=5$, second card can be $2$ or $8$ (2 valid) - For $x=6$, second card can be $3$ (valid) - For $x=7$, second card can be $4$ (valid) - For $x=8$, second card can be $5$ (valid) Total favorable pairs = $1 + 1 + 1 + 2 + 2 + 1 + 1 + 1 = 10$. 5. **Calculating probability:** $$\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{10}{64} = \frac{5}{32}$$ 6. **Final answer:** The probability that the absolute difference between the two numbers drawn is 3 is $\boxed{\frac{5}{32}}$.