Italy at bookmaker odds of is
Similarly for Bulgaria
A newspaper article preceeding the 1994 World Cup semifinal match between Italy and Bulgaria stated that "Itality is favored 10-11 to beat Bulgaria, which is rated at 10-3 to reach the final". Suppose this means that the odds that Italy wins are 11/10 and the odds that Bulgaria wins are 3/10. Find the probability that each team wins, and comment.
Okay, so I know the transformation from Odds to Probability is given by:
Probability = Odds / 1 + Odds
and the transformation from Probabilities to Odds is given by:
Odds = Probability / 1 - Probability
Plugging in, I get:
Probability Italy wins: 0.23
Probability Bulgaria wins: 0.52
Comment: So, from the question, it sounds like Bulgaria is less likely to win given the odds. However, if we calculate the probabilities, its clear that Bulgaria actually has a better shot at winning.
Is this how you would approach the question? I found it a bit easy, I'm afraid I've missed something or interpreted it in a different way.