98 karma · joined April 28, 2008
It depends. The $100 knife could become lost, stolen or damaged. Improved or cheaper knives, or even a new technology to replace the knife as we know it, could appear in the next 30 years. You could even keep two cheap knives so you have a spare whilst the other is in the dishwasher.
The odds are 50%, do you seriously think different?
Your mistake is that in families 1-250 the girl next to the mother could be either daughter.
In families 1-750 there are 1000 daughters, the daughter standing next to the mother is equally likely to be any of those and half have brothers, half have sisters.
I now put the coins back into my pocket, shuffle them about, and again take them out inside my hands. This time I look inside both my hands, not letting you see, and tell you (truthfully) that at least one is tails. Given that information, you can deduce three mutually exclusive possibilities each of equal probability - both are tails, only the coin in my right hand is tails or only the coin in my left hand is tails. Hence we have the odds in this situation of 2/3 for a head/tail combo.
It is easy to see that the first situation is akin to knowing that a particular child is female, whilst the second is akin to knowing that at least one of the children is female. Also, in either case it does not matter if the coins are distinguishable - one could be a euro and the other a pound.
It makes no difference if they have distinguishing marks or not. It matters if you are told that a particular child is a girl (50%) or if you are only told that at least one child is a girl (66%).
BodySpace on bodybuilding.com, which does this, currently has over 200,000 active members - so quite a few actually.