Question

Every year, the New England Patriots play 6 games against teams inside of their
own division (the AFC East), 4 games against teams from the NFC, and 6 games
against other teams in the AFC. We know that the Patriots win 50% of their
games against teams in the NFC, 60% of their games against other teams in the
AFC (but not in the AFC East), and 70% of their games against teams in the
AFC East. The Patriots won their most recent game. What is the probability
the game was against a team that does not play in the AFC East?

Answer 1

P(team not from AFC east | win) = P(team from AFC or NFC | win)

using bayes theorem :

P(team from AFC or NFC | win) = [P(win | team from NFC)*P(team from NFC) + P(win | team from AFC)*P(team from AFC)] / P(win)

{

P(win) = P(win | team from NFC)*P(team from NFC) + P(win | team from AFC)*P(team from AFC) + P(win | team from AFC east)*P(team from AFC east)

= 0.50*4/16 + 0.60*6/16 + 0.70*6/16

P(win) = 0.6125

}

P(team from AFC or NFC | win) = [ 0.50*4/16 + 0.60*6/16 ] / 0.6125 = 0.5714

P(team from AFC or NFC | win) = 0.5714

P.S. (please upvote if you find the answer satisfactory)