Problem:
Selecting a player in your team.
You are the captain of basketball team and have to make decision of playing five. Four players are already selected and you have to make decision among three players named Andrew, Jack and Matt. Assume that only one will be selected and others wont be not even in the team squad.
Don't confuse yourself with the term playing five, you just have to take decision whom to include in the team. Again only ONE will be selected among three.
This is "do or die" game for your team. If you win, you reach the finals otherwise out of the tournament.
There can be following three situations after the end of the tournament:
1. Your team loses this game and doesn't make to the finals.
2. You win the game and reach finals but lose in the finals.
3. You win this game and then win finals.
Winner of the tournament gets prize money of $100,000 and runners-up get $50,000 as prize money. If you don't make to the finals, you win nothing.
Based on their statistics and their abilities, you have some data about each player.
Andrew: If Andrew plays, there is a 20% chance you don't make to the finals, 60% chance that you make to the final but lose in finals and 20% chance of winning the finals.
Jack: If Jack plays, there is a 20% chance you don't make to the finals, 70% chance that you make to the final but lose in finals and 10% chance of winning the finals.
Matt: If Matt plays, there is a 30% chance you don't make to the finals, 45% chance that you make to the final but lose in finals and 25% chance of winning the finals.
Final decision will be yours and you make decision based on the expected value from each player. Create a decision tree and analyze the data.
Solve the problem and show all work.