3. Students $A$ and $B$ each have 3 cards. They play a game by tossing a fair coin, and the game ends when a head appears. What is the probability that the game ends exactly after 5 coin tosses? $\qquad$
3. $\frac{3}{16}$ Detailed Explanation: Toss a coin 5 times. If $A$ wins, then among the first 3 tosses, there is exactly one tail, and the remaining 4 tosses are all heads; if $B$ wins, then among the first 3 tosses, there is exactly one head, and the remaining 4 tosses are all tails. Therefore, the required probability is $P=\frac{3+3}{2^{5}}=\frac{3}{16}$.