Thanks to Data for having generously chosen to forgo his justly earned prize for OT - 7/9/2010 Puzzle, those points (in addition to the book) have been rolled over.
This is a completely straightforward (although rather difficult) probability puzzle. Nothing up my sleeves this time ...
Inspired by this thoughtful assertion:Given:
- 81 home games only, ignore away and postseason games
- Same (constant) win probability for each home game
- Prior win probability is Beta distributed
Prior assumptions:
- You're 95% confident that the Yankees will win at least 50 home games.
- You expect the Yankees to win 58 games
Q: If the Yankees lose their 1st 10 home games, what's the probability they'll still win 50 or more home games over the season?