M14 #29 - soccer game probability

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Re: M14 #29 - soccer game probability [#permalink]

20 Jun 2011, 09:26

THERE ARE 2 C AND 3 T
NUMBER OF OPTINS:
5!/3!*2!

T CAN BE FIRST IN 4 OPTIONS:
TCCTT
TTCCT
TTTCC
TCTCT

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Re: M14 #29 - soccer game probability [#permalink]

07 Nov 2011, 09:30

Total possibilities for the first goal are=5
Total possibilities the loser team has the first goal=2

probability= \frac{2}{5}

Answer: C

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Re: M14 #29 - soccer game probability [#permalink]

21 Jun 2012, 05:57

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It's a number's game. To fill the first slot, the losing team has a 2 in 5 chances of having scored the first goal, since there are 5 goals in total and 2 goals were scored by the loser.

Alternatively, the total arrangements of goals can be seen as WWW (3 goals for the winning team) and LL (2 goals for losing team). The total number of ways of arranging WWWLL, taking account of identical items is 5!/ (3!*2!)=10 ways.

Since the first spot goes to the losing team, there will be a total of 4 goals to be arranged (WWWL) and the number of ways is 4!/(3!)= 4 ways.

Therefore probability of losing team scoring first is # favorable outcomes/# total possible outcomes = 4/10 = 2/5.

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Re: M14 #29 - soccer game probability [#permalink]

21 Jun 2012, 22:24

Hi All

I choose 1/2 .. here probability is for loser team. why the score of winning team need to be considered so it will be 1 out of 2 goals ..

Can u plz explain me

Thank u
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Re: M14 #29 - soccer game probability [#permalink]

22 Jun 2012, 01:42

MBACHANGE wrote:

Hi All

I choose 1/2 .. here probability is for loser team. why the score of winning team need to be considered so it will be 1 out of 2 goals ..

Can u plz explain me

Thank u

If a certain soccer game ended 3:2, what is the probability that the side that lost scored first? (Assume that all scoring scenarios are equiprobable)

A. \frac{1}{4}
B. \frac{3}{10}
C. \frac{2}{5}
D. \frac{5}{12}
E. \frac{1}{2}

Consider empty slots for 5 goals: *****. Say W is a goal scored by the winner and L is a goal scored by the loser. We need the probability that when distributing these goals (5 letters LLWWW) into 5 slots L comes first.

Since there are 2 L's out of total 5 letters then P=Favorable/Total=2/5.

Answer: C.

Hope it's clear.
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Re: M14 #29 - soccer game probability [#permalink]

22 Jun 2012, 02:10

Thanks bunel

what if question was loser team scored second goal instead of first goal. then also it will 2/5 rgt? and if winning team scored first, second or third goal will be 3/5

Regards

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Re: M14 #29 - soccer game probability [#permalink]

22 Jun 2012, 02:16

MBACHANGE wrote:

Thanks bunel

what if question was loser team scored second goal instead of first goal. then also it will 2/5 rgt? and if winning team scored first, second or third goal will be 3/5

Regards

Regards

Absolutely, the probability that the loser team scored the first, second, ..., fifth goal is the same and equals to 2/5 and the probability that the winner team scored the first, second, ..., fifth goal is the same and equals to 3/5.

Check similar questions to practice:
a-box-contains-3-yellow-balls-and-5-black-balls-one-by-one-90272.html
each-of-four-different-locks-has-a-matching-key-the-keys-101553.html
a-box-contains-3-yellow-balls-and-5-black-balls-one-by-one-105990.html
a-bag-contains-3-white-balls-3-black-balls-2-red-balls-100023.html

Hope it helps.
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Re: M14 #29 - soccer game probability [#permalink]

24 Jun 2012, 00:33

I couldnt work it at all

thanks for the explanation guys!
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Re: M14 #29 - soccer game probability [#permalink] 24 Jun 2012, 00:33

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M14 #29 - soccer game probability

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M14 #29 - soccer game probability

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