Who Goes First?

A shooting contest has two stages, and each team consists of two players. In stage one, one team member shoots $3$ times; if all $3$ shots miss, the team is eliminated with score $0$; if at least one shot succeeds, the team advances to stage two, where the other member shoots $3$ times, scoring $5$ points per successful shot and $0$ otherwise. The team's score is the total from stage two. A team consists of players $1$ and $2$; player $1$ succeeds on each shot with probability $p$ and player $2$ with probability $q$, all shots independent.

1. If $p = 0.4$ and $q = 0.5$ and player $1$ shoots in stage one, find the probability that the team scores at least $5$ points. 2. Assume $0 < p < q$.

1. To maximize the probability that the team scores exactly $15$ points, who should shoot in stage one?
2. To maximize the expected value of the team's score, who should shoot in stage one?