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PostPosted: Sun Nov 25, 2007 11:50 am 
Hi
Can anyone help to explain the workings to the answer to the following probability question.

There are 12 boys and 8 girls in a class, including a brother and a sister. If one boy and one girl are chosen at random from the boys and girls respectively, what is the probability that the brother and sister are both chosen?

Ans = 1/190


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 Post subject: Amended question
PostPosted: Sun Nov 25, 2007 11:55 am 
Sorry, I posted the wrong question. It is re-presented below, can anyone show how to arrive at the answer:

There are 12 boys ans 8 girls in a class, including a brother and sister. If 2 pupils are chosen at random from the class, what is the probability that the brother and sister are both chosen?

Ans = 1/190


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 Post subject:
PostPosted: Sun Nov 25, 2007 12:32 pm 
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Joined: Fri Mar 17, 2006 5:12 pm
Posts: 1300
Location: Birmingham
Lets call the Brother Child A and the sister Child B.

The chance of selecting A from the class is 1/20 and the chance of selecting B from the remainer is 1/19. So the chance of selecting A followed by B is 1/20 x 1/19 = 1/390.

But you have to consider the other alternative valid option which is selecting B first followed by A which is also 1/390.

Therefore the chance of selecting AB or BA is therefore 2/390 = 1 in 190.


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 Post subject:
PostPosted: Sun Nov 25, 2007 12:34 pm 
Hi KenR

Many thanks for your help..

Just as well I am not sitting 11+.


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 Post subject:
PostPosted: Sun Nov 25, 2007 2:56 pm 
1/195 ??


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PostPosted: Sun Nov 25, 2007 3:09 pm 
Hi KenR.

If you can help on this last probability question, it would be much appreciated. I will also include my (incorrect) workings so far.

In a drawer are 3 black socks and 2 white socks. If 2 are picked at random, what is the probability that they will be the same colour?
Ans = 2/5

My workings:

Let Black = B, and White = W

Probability of getting one black, B = 1/5

Probability of getting one white from the remainder, C= 1/4

Therefore

Probability of getting 2 black socks = 2 times 1/5 = 2/5

Probability of getting 2 white socks socks = 2 times 2/4 =1/2


Therefore probaility of getting either 2 white socks or 2 blacks socks is:

2/5 times 1/2 = 2/10 = 1/5 = incorrect answer

Can you please help?


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 Post subject:
PostPosted: Sun Nov 25, 2007 3:24 pm 
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Joined: Mon Feb 12, 2007 1:21 pm
Posts: 11931
Two way of getting a pair BB or WW

prob (BB) = 3/5 x 2/4 (2 of the four socks left are black) = 6/20

prob (WW) = 2/5 x 1/4 (only 1 of the remaining socks is whaite) = 2/20

Total = 8/20 = 2/5

Hope this helps!


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 Post subject: Probability
PostPosted: Sun Nov 25, 2007 3:28 pm 
Guest 55,

You have literally just beaten me to it. I was about to submit the very same solution.

C


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 Post subject:
PostPosted: Sun Nov 25, 2007 3:32 pm 
Hi Guest55. Many thanks for your help.


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 Post subject:
PostPosted: Sun Nov 25, 2007 4:36 pm 
Is this an 11+ question!!!! :shock: :shock:


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