D H Posted July 30, 2010 Share Posted July 30, 2010 For this problem, please ignore the fact that babies are not 50-50 boys-girls. Just assume that half of all babies are boys, the other half girls. A starter question first. You meet two old friends. One says "I have two children. The older one is a boy". The other says "I have two children, too, and at least one of them is a boy." For each friend, what is the probability that both of their children are boys? Hint: The probabilities are different. Now a third old friend joins up with you and says "I also have two children. One is a boy who was born on a Tuesday." What is the probability that both of this third friend's children are boys? Link to comment Share on other sites More sharing options...
Mr Skeptic Posted July 30, 2010 Share Posted July 30, 2010 [hide]For the first, there's a 1 in 2 chance that both are boys. The first child is known to be a boy, and there is a 1 in 2 chance that the next will be a boy.[/hide] [hide]For the second, there's a 1 in 3 chance that both are boys. There are 4 possibilities for 2 children, each equally likely, but the possibility that both are girls is eliminated. Thus there remain 3 possibilities equally likely, and only 1 of them has both children as boys.[/hide] [hide]For the third, there's a 13 in 27 chance that both are boys. The trick is to be sure not to double-count the possibility of both boys being born on a Tuesday.[/hide] Link to comment Share on other sites More sharing options...
DJBruce Posted July 31, 2010 Share Posted July 31, 2010 (edited) Person 1 has a .5 chance that both his children are boys. The possible pairs for two children are (Please note the B=Boy, G=Girl, The left one represents the older child): GB GG BG BB Since we know the first one is a boy then you reduce the number of possibilities to: BG BB Which means that in 1 out of the 2 scenarios Person 1 has all boys Person 2 has a 1/3 chance of having all boys. Again the possible pairs for the sex of two children are: GB GG BG BB Since we know at least one of the children is a boy you can eliminate the possibility that both children are girls. This then leaves you with GB BG BB So out of the three options only one occurs were Person 2 has all boys For the third person there is a 13/27 chance both are boys. To see why look at the attached PDF where I list all the possible permutations, and then highlighted the ones which give you two boys. Warning do not look at the file if you do not want a spoiler to number 3.Born on Tuesday.pdf Edited July 31, 2010 by DJBruce Link to comment Share on other sites More sharing options...
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