Question

There is a football game between two rival teams -- Team 0 and Team 1. Suppose Team 0 wins 65% of the time and Team 1 wins the remaining matches. Among the games won by Team 0, only 30% of them come from playing on Team 1’s football team. On the other hand, 75% of the victories for Team 1 are obtained while playing at home. If Team 1 is to host the next match between the two teams, which team will most likely emerge as the winner?

Answer 1

Solution:

Let X be the team hosting the match and Y be the winner of the match. Both X and Y can take on values
from the set {0,1}. Then:
Probability Team 0 wins is P(Y= 0) = 0.65.
Probability Team 1 wins is P(Y= 1) = 1 = 1 − 0.65 = 0.35.
Probability Team 1 hosted the match it won is
P(X =1|Y = 1) = 0.75.
Probability Team 1 hosted the match won by Team 0 is
P(X = 1|Y = 0) = 0.3.

Clearly Team 1 will most likely will emerge as the winner if team 1 host the match