A shooting competition is divided into two stages. Each participating team consists of two members. The specific rules are as follows: In the first stage, one team member shoots 3 times. If all 3 shots miss, the team is eliminated with a score of 0. If at least one shot is made, the team advances to the second stage, where the other team member shoots 3 times, earning 5 points for each made shot and 0 points for each missed shot. The team's final score is the total points from the second stage. A participating team consists of members A and B. Let the probability that A makes each shot be $p$, and the probability that B makes each shot be $q$. Each shot is independent. (1) If $p = 0.4$ and $q = 0.5$, with A participating in the first stage, find the probability that the team's score is at least 5 points. (2) Assume $0 < p < q$. (i) To maximize the probability that the team's score is 15 points, who should participate in the first stage? (ii) To maximize the expected value of the team's score, who should participate in the first stage?
(1) $P = (1 - 0.6^3)(1 - 0.5^3) = 0.686$. (2)(i) Person A should participate in the first stage. Since $P_{\text{A first}} - P_{\text{B first}} = 3pq(p-q)(pq-p-q) > 0$. (ii) Person A should participate in the first stage. $E(X) - E(Y) = 15(p-q)pq(p+q-3) > 0$ since $p-q < 0$ and $p+q-3 < 0$.
A shooting competition is divided into two stages. Each participating team consists of two members. The specific rules are as follows: In the first stage, one team member shoots 3 times. If all 3 shots miss, the team is eliminated with a score of 0. If at least one shot is made, the team advances to the second stage, where the other team member shoots 3 times, earning 5 points for each made shot and 0 points for each missed shot. The team's final score is the total points from the second stage. A participating team consists of members A and B. Let the probability that A makes each shot be $p$, and the probability that B makes each shot be $q$. Each shot is independent.\\
(1) If $p = 0.4$ and $q = 0.5$, with A participating in the first stage, find the probability that the team's score is at least 5 points.\\
(2) Assume $0 < p < q$.\\
(i) To maximize the probability that the team's score is 15 points, who should participate in the first stage?\\
(ii) To maximize the expected value of the team's score, who should participate in the first stage?