Quote:
Originally Posted by LazyScot
Actually, I think this moving us on.
The first answer of 1/4, I'm confident of, since that is based on the importance of order (something tells me this is related to the difference between permutations and combinations....)
Anyhow, my first attempt at the second answer ignored order, and I think that was wrong, whereas yours did take it into account. Thus I think that the second answer should be 1/3 as the possibilities are BB BG GB.
If we were to expand the possibilities up each pair would come out to 49 possibilities. B(monday)B(monday), B(monday)B(tuesday), etc. However, we know that at least one boy was born on a tuesday, so the BG can only be expanded up to 7 possibilities each. B(tuesday)G(monday) and so on. By comparison, the BB expands up to 14 possibilities. So we have a total of 28 possibilities.
So the answer to 3 is, I think 1/2. (i.e. 14 out of 28)
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I counted the B(tuesday)B(tuesday) twice. So the BB should expand to 13 possibilities. Hence a total of 13 out 27.
Quote:
Originally Posted by omk3
Ok next try.
We have three possible combinations, GB, BG, BB.
The chances of the boy being born on a Tuesday on each of the first two cases is 1/7.
In the BB case, we have 49 possible combinations, in 13 of which there is at least on Tuesday. So the chances of at least on boy being born on a Tuesday in a BB case are 13/49.
Which makes the overall probability.... 
...13/27?
Oh how I wish I remembered how to calculate these things... |
Quote:
Originally Posted by pdurrant
Yes! We have a winner! 13/27 is indeed the right answer.
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So can you confirm if my logic is right, or have I committed the ultimate sin (according to my old Maths teacher) of getting the right answer for the wrong reason...