percentage question

chicom

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Jun 17, 2009
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hi, i need a little bit of help with percentages.

okay so here is my problem: I need to find a percentage number out of this.

two sporting teams are playing each other. Team A vs team B.

I want to know that if Team A wins, what percentage chance the team has of winning by over 40 points or by under 40 points. Or if team A loses what percentage chance the team has of losing by over/under 40. The same goes for team B.

Okay so i've worked out that if team A wins, they have on average an 80% chance of winning by under 40 points (that is an average based on their results against every team in the competition). Needless to say they therefore have a 20% chance of winning by over 40 points in general when they win.

Team B when they lose, most of the time they lose by under 40 points (91% of the time), while losing 9% of the time by over 40 when they lose.

My question is if these two teams are playing each other, if team A were to win, what % chance would it have of winning by under 40 points and what % by over 40?

Clearly there is a high percentage chance of team A winning by under 40 as they generally win by under this margin, 80% of the time, and when team B lose they lose by under 40 points 91% of the time. But what is the exact percentage and how do i obtain it? Obviously the answer im after should mean that team A's chance of winning by under 40 should match that of team B's chance of losing by under 40.

Im hoping it is a very easy process however for some reason i cannot find an answer! any help is greatly appreciated!
 
There's not really enough info to give a firm answer.

Let D be the event that "the goal difference is less than 40"
Let A be the event that "A plays and wins"
Let B be the event that "B plays and loses"

You have P(D|A) = 0.8, P(D|B) = 0.91, and you want P(D|A and B).

Now,
P(D|A) = P(A and D) / P(A),
P(D|B) = P(B and D) / P(B),
P(D|A and B) = P(A and B and D)

Also, P(A and B and D) = P(A and D) + P(B and D) - P(A or B, and D)

But I think this is not very useful.... if you can find P(A and B and D), you would already have worked out P(D|A and B) yourself...
 
thanks dr.mike, you got me thinking some more about it and i think i've got a fair idea now about what to do!
 
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