6. Let $A=\{1,3,5,7,9\}, B=\{2,4,6,8\}$. Now, by tossing a coin, numbers are drawn without replacement from $A$ and $B$ to form a nine-digit number. The rule is: if the coin shows heads, the smallest number from set $A$ is taken; if the coin shows tails, the smallest number from set $B$ is taken. When the numbers from one set are exhausted and the other set still has numbers, the remaining numbers from the other set are added in ascending order. According to this rule, the probability that the drawn numbers are exactly 123456789 is . $\qquad$
6. $\frac{1}{256}$.

According to the rule, the sequence of heads and tails from tossing a coin is:
heads-tails-heads-tails-heads-tails-heads-tails.
Therefore, the probability of drawing the number sequence 123456789 is
$$
\left(\frac{1}{2}\right)^{8}=\frac{1}{256} \text {. }
$$