A Probability Brain Teaser
June 4th, 2008
A little probability brain teaser for all of you… I was given this last week and I’m still having problems working out what the answer is!
A family has 2 children. When you knock on the door one of the children, a boy, opens the door. What is the probability that the other child is a boy?
I’ve got an answer in my head but I can’t quite figure out which one is correct so it would be great to hear your thoughts on what you think the answer is!
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It sounds a bit like a reworking of the Monty Hall problem… but as to what the answer is I’m not entirely sure (I’d hazard a guess at 1/3?)
I watched a good TED talk the other day though on probability and statistics and stuff which you might find interesting: http://www.ted.com/index.php/talks/view/id/67
It should be 50%.
50%. That the first child is a boy doesn’t affect the odds. Before the door was opened it was a 1/3 possibility that both of the children were boys. But when it turns out that the first child was a boy the odds goes up to 50% that both of the children are boys.
I think it is only “Monty Hall” if there is additional selection material, the decision to open the empty box - in this case something like “boys must answer the door before girls”. Therefore, as Robin says the odds of the sex of the second child don’t change
[...] few days ago I posted a probability brain teaser which was getting me in a spin. A family has 2 children. When you knock on the door one of the [...]
Hi,
Thanks for the comments everyone! I’m still torn between a third and a half… see my follow up at http://cow.neondragon.net/index.php/probability-brain-teaser-ii
I think you might have hit upon something Toby. But the question essentially states that a boy did open the door first.