Probabillities in the World Cup

[Hepic]

I was watching yesterday my county(Greece) in international cup,and I thought something about probabillities. Let's say, that two football games take place the same time. In the first game, the team that we want to win has 30% to win,and in the second game the team that,we want to win has 20% to win.

I think that the probabillities to win both team are 6%,and the probabillities to win one or both teams are 44%.

I am correct??

(Two differents games,with four differents teams.)

 

[Simon Bridge]

Please state your reasoning and show your working ;)

 

[verty]

It depends. If your team wins the first game, the chances of winning the second game go down because the other team won't want to lose both, they'll play aggressively and may put their best players on. But if the first game is a draw, the second will be easier to win. So there's not a clear answer to this question without knowing the conditional probabilities.

 

[Simon Bridge]

It depends. If your team wins the first game, the chances of winning the second game go down because the other team won't want to lose both, they'll play aggressively and may put their best players on. But if the first game is a draw, the second will be easier to win. So there's not a clear answer to this question without knowing the conditional probabilities.

In the problem statement it says...

Let's say, that two football games take place [at] the same time.

The two games are taking place at the same time - in each game we have a favorite team.
i.e. in the first game it may be Greece vs Spain - and we prefer Greece to win; and in the second game it is New Zealand vs Australia, and we prefer New Zealand to win.

How would the result of one game affect the result of the other one?

 

[Borek]

How would the result of one game affect the result of the other one?

Players know what is going on on the other stadium, so they change their tactics accordingly. If the result of the other game is good for them they won't press that hard, if the result is bad, they try hard to score. Happens all the time. Thus I don't think the assumption that win probability for each team is constant.

But perhaps we are trying to solve life-like problem, instead of much simpler, _rigid_ problem defined by OP.

 

[Simon Bridge]

You mean the win probability could change during the game?
That's actually a given, even if the players don't know what happens in the other stadium.

Need the feedback from Hepic.

 

[verty]

Same time, no information, then it is indeed very much simpler.