In the depths of a drawer, there are three pairs of socks that are slightly different from each other. By fishing the socks out of the drawer one by one, what is the probability that after three draws, there will not be a matching pair among the socks taken out?
From the 6 socks in the drawer, we pull out one of the pair's pieces on the first draw. The probability that the second draw does not result in the other half of this pair is $\frac{4}{5}$, since 5 socks remain, and 4 of them are not the match to the first one.

For the third draw, 4 socks remain in the drawer, consisting of one pair and two half-pairs, and we must draw a sock that does not match the previous ones. This is possible if we draw one of the remaining pair. The probability of this is: $\frac{2}{4}$.

Therefore, the probability that after 3 draws, there is still no matching pair is: $\frac{4}{5} \cdot \frac{2}{4}=\frac{2}{5}$.

Pajna Gabriella (Debrecen, Tóth Á. Gymn., 10th grade)