x̄ - > To determine the updated probabilities of each team winning the tournament

To determine the updated probabilities of each team winning the tournament, we need to consider the original probabilities and the current stage of the tournament. We have the following semi-final matchups:

- Uruguay vs. Colombia

- Argentina vs. the winner of Uruguay vs. Colombia

Given the original probabilities:

- Argentina: 30%

- Brazil: 25%

- Uruguay: 14%

- Colombia: 6%

Since Brazil is not in the semi-finals, their probability is now 0%.

First, we will update the probabilities based on the semi-final matchups. To do this, we will calculate the probability of each team winning their match and then the tournament.

### Probabilities Before the Semi-Finals

- Argentina: 30%

- Uruguay: 14%

- Colombia: 6%

- (Brazil: 25%, now 0%)

### Semi-Finals

#### Uruguay vs. Colombia

- Uruguay's probability of winning: 14% / (14% + 6%) = 70%

- Colombia's probability of winning: 6% / (14% + 6%) = 30%

### Final

If Uruguay wins against Colombia:

- Probability of Uruguay winning the tournament: Probability of winning semi-final * (Original probability / (Original probability of all remaining teams))

  - Uruguay's updated probability: 70% * (14% / (14% + 30%)) = 24.14%

If Colombia wins against Uruguay:

- Probability of Colombia winning the tournament: Probability of winning semi-final * (Original probability / (Original probability of all remaining teams))

  - Colombia's updated probability: 30% * (6% / (6% + 30%)) = 5.45%

Now, we consider Argentina in the final:

- Probability of Argentina winning the tournament: Original probability / (Original probability of all remaining teams)

  - Argentina's updated probability: 30% / (30% + 14% + 6%) = 30% / 50% = 60%

### Combined Probabilities

To find the overall updated probabilities for each team, we combine the probabilities of winning the semi-finals and the finals.

- Argentina:

  - Probability of reaching the final: 100% (as they are already in the final)

  - Probability of winning the final: 60%

  - Overall probability: 60%

- Uruguay:

  - Probability of reaching the final: 70%

  - Probability of winning the final: 24.14%

  - Overall probability: 70% * 24.14% = 16.9%

- Colombia:

  - Probability of reaching the final: 30%

  - Probability of winning the final: 5.45%

  - Overall probability: 30% * 5.45% = 1.6%

### Final Probabilities

- Argentina: 60%

- Uruguay: 16.9%

- Colombia: 1.6%

Thus, the updated probabilities for each team winning the tournament are:

- Argentina: 60%

- Uruguay: 16.9%

- Colombia: 1.6%

Colombia have a tough match against Uruģuay having won only 14 times, drawn 11 and lost 22 against them.

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