13. There are two bags, $A$ and $B$. Bag $A$ contains 6 cards, one of which is labeled 0, two are labeled 1, and three are labeled 2; Bag $B$ contains 7 cards, four of which are labeled 0, one is labeled 1, and two are labeled 2. One card is drawn from bag $A$ and two cards are drawn from bag $B$, making a total of three cards. Find:
(1) The probability that all three cards drawn are 0;
(2) The probability that the product of the numbers on the three cards is 4.
13. (1) $P=\frac{C_{1} C_{4}^{2}}{C_{6} C_{7}^{3}}=\frac{1}{21}$;
(2) $P=\frac{C_{2} C_{2}^{2}+C_{3} C_{1} C_{2}^{1}}{C_{6} C_{3}}=\frac{4}{63}$.
12. $\frac{3}{34}$ Let $p$ be the probability of the first flip being heads and meeting the condition, and $q$ be the probability of the first flip being tails and meeting the condition, then $q=\frac{1}{2} p$, because a tails must be followed by a heads. $p=\frac{1}{2} q+\frac{1}{4} q+\frac{1}{8} q+\frac{1}{16} q+\frac{1}{32} q$, solving this gives: $p=\frac{1}{17}, q=\frac{1}{34}$.