Sean's Problem #2: SBL
LOEL
There is a baseball league called SBL (Seanny Baseball League), which had five teams (The Wolves, The Phoenixes, The Buffaloes, The Swallows, The Pandas).  Three players in the league are Cody Trout, Mike Cole, and Gerrit Bellinger in the Pandas, Wolves, and the Swallows, respectively. They have been playing in their teams for three years. The after-season rules are:

1. Every player must stay in their team, move to another team, or retire. One can switch teams only once every season.
2. If a player joined two years ago or earlier on the team, the probability of him moving to another team is 0.1.
3. If a player joined three years ago or later on the team, the probability of him moving to another team is 0.25.
4. If a player leaves a team, the probability of going to each other team is the same for all (or 0.25 probability for each team)
5. A player can only retire after a minimum of 13 years of experience.
6. After one's 13th year, the probability of him retiring is 0.1, and that number increases by 0.1 every year (so, after one's 22nd year, a player is certainly going to retire).
7. For the next 5 years after one's retirement, they have a 0.05 chance of coming back. When it has been over five years since one's retirement and he didn't come back, he can not return ever again.
8. When a player comes back, they will have an equal probability of going to every team, and they will play 3 years before they retire again for good (no returning).
10. If a player who has come back from retirement returned in their old team, their year count in the team will continue from before the retirement.
11. If a player who has come back from retirement returned not in their old team, their year count of the team will start again from 1.
12. Mike Cole is in his 6th year. Gerrit Bellinger is in his 8th year. Cody Trout is in his 3rd year.

QUESTIONS
1. What is the probability that Mike Cole and Gerrit Bellinger will be on the same team next year?
2. What is the probability that Cody Trout and Gerrit Bellinger will not be on the same team next year?
3. What is the probability that all three players will be on a team starting with the letter three years later? (Pandas, Phoenixes)
4. What is the probability that at least one player will be on the Buffaloes three years later?
5. What is the probability that none of the three players will have retire ten years later?
6. What is the probability that at least one player has come back from retiring?
7. What is the probability that all three players will be put in either Wolves or Pandas 14 years later?
8. What is the probability that one player has retired a second time, one player has retired but came back on a different team, and one player has not retired 15 years later?
9. What is the probability that at least two players will have been in at least six teams in 12 years?
10. What is the probability that all three players have retired a second time below their 21st year?
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LOEL
I created this one.
LOEL
Nope
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