3. There are 5 red balls and 5 black balls numbered $1,2,3,4,5$ respectively. If 4 balls are drawn from them, the probability that the numbers on the balls drawn are all different is $\qquad$
3. $\frac{8}{21}$.

From 10 balls, choosing 4, there are $\mathrm{C}_{10}^{4}=210$ different ways. If it is required that the numbers of the chosen balls are all different, one can first select 4 numbers from 5 numbers, which has $\mathrm{C}_{5}^{4}$ ways. For each number, there are two colors to choose from, so the number of ways to pick balls with all different numbers is $\mathrm{C}_{5}^{4} \cdot 2^{4}=80$. Therefore, the probability of picking balls with all different numbers is $\frac{80}{210}=\frac{8}{21}$.