Probability in a football game
- Fahim Shahriar
- Posts:138
- Joined:Sun Dec 18, 2011 12:53 pm
There is match between $A$ and $B$.
Formation of team $A$ $(3-4-3)$ and Team $B$ $(2-4-4)$.{That means team $B$ has 2 strikers,4 mid-fielders and 4 defenders.}
In this game, only the strikers and the mid-fielders can score goals. But the mid-fielders can't score more than $1$ goal.
Now, Team $A$ will score 4 goals and Team $B$ will score 3 goals.
Player of which team has better probability of making a HAT-TRICK ?
Formation of team $A$ $(3-4-3)$ and Team $B$ $(2-4-4)$.{That means team $B$ has 2 strikers,4 mid-fielders and 4 defenders.}
In this game, only the strikers and the mid-fielders can score goals. But the mid-fielders can't score more than $1$ goal.
Now, Team $A$ will score 4 goals and Team $B$ will score 3 goals.
Player of which team has better probability of making a HAT-TRICK ?
Name: Fahim Shahriar Shakkhor
Notre Dame College
Notre Dame College
- Fahim Shahriar
- Posts:138
- Joined:Sun Dec 18, 2011 12:53 pm
Re: Probability in a football game
This is a self-made problem. I got the idea of making such problem while playing FIFA game. Adding some conditions, I tried to make it an interesting one.
Name: Fahim Shahriar Shakkhor
Notre Dame College
Notre Dame College
- kfoozminus
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Re: Probability in a football game
Team-$A$
jannatul ferdows jenny
https://sites.google.com/site/mathprogrammingbooks/
https://sites.google.com/site/mathprogrammingbooks/
- Fahim Shahriar
- Posts:138
- Joined:Sun Dec 18, 2011 12:53 pm
Re: Probability in a football game
My solution is nothing but a huge calculation.
For Team $A$, when the 3 strikers scored all the goals,there are the possibilities how they can score goals.
[number of possibilities has been marked in () and hat-trick as {H}]
4-0-0 »(3) ways {H}
3-1-0 »(6) {H}
2-2-0 »(3)
2-1-1 »(3)
Now when the midfielders score only 1 goal, strikers score 3 goals as follows.
3-0-0 »3 {H}, midfielders 4 ways. (12 ways)
2-1-0 »6 (24)
1-1-1 »1 (4)
Finally, I got A»21/104 & B»1/16
For Team $A$, when the 3 strikers scored all the goals,there are the possibilities how they can score goals.
[number of possibilities has been marked in () and hat-trick as {H}]
4-0-0 »(3) ways {H}
3-1-0 »(6) {H}
2-2-0 »(3)
2-1-1 »(3)
Now when the midfielders score only 1 goal, strikers score 3 goals as follows.
3-0-0 »3 {H}, midfielders 4 ways. (12 ways)
2-1-0 »6 (24)
1-1-1 »1 (4)
Finally, I got A»21/104 & B»1/16
Name: Fahim Shahriar Shakkhor
Notre Dame College
Notre Dame College
- kfoozminus
- Posts:33
- Joined:Mon Nov 26, 2012 4:52 pm
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Re: Probability in a football game
find my fault...
jannatul ferdows jenny
https://sites.google.com/site/mathprogrammingbooks/
https://sites.google.com/site/mathprogrammingbooks/
- Fahim Shahriar
- Posts:138
- Joined:Sun Dec 18, 2011 12:53 pm
Re: Probability in a football game
There is a little misunderstanding.
I meant each of mid-fielders can't score more than 1 goal.
I meant each of mid-fielders can't score more than 1 goal.
Name: Fahim Shahriar Shakkhor
Notre Dame College
Notre Dame College
- kfoozminus
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Re: Probability in a football game
i did consider this condition!Fahim Shahriar wrote:There is a little misunderstanding.
I meant each of mid-fielders can't score more than 1 goal.
jannatul ferdows jenny
https://sites.google.com/site/mathprogrammingbooks/
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- nafistiham
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Re: Probability in a football game
Why is that ?kfoozminus wrote:find my fault...
what if each mid fielder scores $1$ goal ?
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
- kfoozminus
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Re: Probability in a football game
thanks for finding the bug... this was so annoying me...
hey, maybe you can look into this too viewtopic.php?f=28&t=2216
i'm not sure about the answer, and looks like nobody's interested in football!
hey, maybe you can look into this too viewtopic.php?f=28&t=2216
i'm not sure about the answer, and looks like nobody's interested in football!
jannatul ferdows jenny
https://sites.google.com/site/mathprogrammingbooks/
https://sites.google.com/site/mathprogrammingbooks/
- Fahim Shahriar
- Posts:138
- Joined:Sun Dec 18, 2011 12:53 pm
Re: Probability in a football game
I couldn't post my full solution because my mobile supports limited texts.
And Alas! My computer is now in hospital for treatment.
.
.
You can say it a joke.
And Alas! My computer is now in hospital for treatment.
.
.
You can say it a joke.
Name: Fahim Shahriar Shakkhor
Notre Dame College
Notre Dame College