You overcount, the both on Tuesday is overcounted there. Think of it this way- if I have 8 kids do I have a better than 100% probability of having a kid born on Tuesday?
There is a 1/7x6/7 chance the first is born on Tuesday and the second is born on another day. There is a 1/7x6/7 chance the second is born on Tuesday and the first is born on another day. And there is a 1⁄49 chance that both are born on Tuesday.
All together thats 13⁄49. Alternatively, there is a (6/7)^2 chance that both are born not-on-Tuesday, so 1-(6/7)^2 tells you the complementary probability.
I’ve seen that same explanation at least five times and it didn’t click until just now. You can’t distinguish between the two on tuesday, so you can only count it once for the pair.
Which means the article I said was wrong was absolutely right, and if you were told that, say one boy was born on January 17th, the chances of both being born on the same day are 1-(364/365)^2 (ignoring leap years), which gives a final probability of roughly 49.46% that both are boys.
Thanks for your patience!
ETA: I also think I see where I’m going wrong with the terminology—sampling vs not sampling, but I’m not 100% there yet.
You overcount, the both on Tuesday is overcounted there. Think of it this way- if I have 8 kids do I have a better than 100% probability of having a kid born on Tuesday?
There is a 1/7x6/7 chance the first is born on Tuesday and the second is born on another day. There is a 1/7x6/7 chance the second is born on Tuesday and the first is born on another day. And there is a 1⁄49 chance that both are born on Tuesday.
All together thats 13⁄49. Alternatively, there is a (6/7)^2 chance that both are born not-on-Tuesday, so 1-(6/7)^2 tells you the complementary probability.
Wow.
I’ve seen that same explanation at least five times and it didn’t click until just now. You can’t distinguish between the two on tuesday, so you can only count it once for the pair.
Which means the article I said was wrong was absolutely right, and if you were told that, say one boy was born on January 17th, the chances of both being born on the same day are 1-(364/365)^2 (ignoring leap years), which gives a final probability of roughly 49.46% that both are boys.
Thanks for your patience!
ETA: I also think I see where I’m going wrong with the terminology—sampling vs not sampling, but I’m not 100% there yet.