Probabiity in Football game.

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Masum
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Probabiity in Football game.

Unread post by Masum » Tue Jun 05, 2012 4:29 pm

The time football game is divided into $18$ equal parts, in each part one team can make at most $1$ goal. Now, find the probability that there will be at least one team to make a prime number of goals.
One one thing is neutral in the universe, that is $0$.

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Fahim Shahriar
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Re: Probabiity in Football game.

Unread post by Fahim Shahriar » Sun Aug 05, 2012 9:43 pm

67/153 :) :)
Name: Fahim Shahriar Shakkhor
Notre Dame College

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Masum
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Re: Probabiity in Football game.

Unread post by Masum » Tue Aug 07, 2012 10:42 am

I should mention it earlier, I didn't notice it. Assume, given the probability of scoring a goal for each team.
One one thing is neutral in the universe, that is $0$.

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kfoozminus
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Re: Probabiity in Football game.

Unread post by kfoozminus » Mon Dec 24, 2012 4:36 pm

Fahim Shahriar wrote:67/153 :) :)
how did you get it? i've got $\frac{63}{703}$ :?
in each part, at most $2$ goals can be made. so, at most $36$ goals can be made in $18$ parts.
after the end of the game, $0$ goal or $1$ goal or $2$ goals or $3$ goals... or $36$ goals can be made totally.

$0$ goal can be made in $1$ way, $1$ goal can be made in $2$ ways($1$ goal per team), $2$ goals can be made in $3$ ways -
$(a)$ $1$st team scored all
$(b)$ $2$nd team scored all
$(c)$ $1$ goal per team

... here we can see that $n$ goals can be made in $n+1$ ways.

so any number of goals can be made in $1+2+3+...+37=\frac{37\cdot38}{2}=703$ ways

there are $7$ prime numbers under $18$. $1$st team can score prime number of goals in $7$ ways. so can $2$nd team. and there are possibilities that each team can make prime number of goals - in $7\cdot7=49$ ways

total ways of prime number of goals$=7+7+49=63$

probability$=\frac{63}{703}$

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Masum
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Re: Probabiity in Football game.

Unread post by Masum » Sat Jan 12, 2013 2:06 am

আসলে উত্তরটা আসবে তাদের গোল করতে পারার প্রোবাবিলিটর সাপেক্ষে। অজটিলতার(!) জন্য ধরে নেওয়া হোক দুই পক্ষেরই ১৮ ভাগে যে কোন এক ভাগে গোল করার প্রোবাবিলিটি সমান।
One one thing is neutral in the universe, that is $0$.

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