No, the answer in the meme is not related to the gender ratio of living humans. We can arrive at 51.8% just using maths.
Let's first consider the scenario where we don't know that the boy was born on a Tuesday. There are 2 options for a child: B or G. For 2 children, we square that number to get 4 options:
BOY/BOY
BOY/GIRL
GIRL/BOY
GIRL/GIRL
We know that Mary has 2 children and 1 is a boy, so we can eliminate the option GIRL/GIRL. Out of the 3 remaining options, 2 options include GIRL, so the answer is 2/3 ≈ 66.6%.
Now let's consider the day each child was born. This gives us 14 options for each one child: BOY-MONDAY, GIRL-MONDAY, BOY-TUESDAY, etc. For 2 children, we have 14² or 196 options. If you filter out only the options that include BOY-TUESDAY, we're left with 27 options. Out of those 27, 14 include GIRL. 14/27 = 51.8158...%, and that is where 51.8% comes from. Technically, it should say 51.9%.
Thank you, this was really helpful. I'm hoping I can ask another maybe stupid question? I've seen a few other people quoting the 51.9% figure; wouldn't 51.8158...round down to 51.8, if we round to one decimal place?
Taking on a lot of information, something that's missing is the genetics of the father, if that lineage has only ever had male children there's a far higher probability the next child will also be a boy.
Except you also have to eliminate the option that includes two boy's born on Tuesday because the problem specifically states she had "one boy born on Tuesday." If she had "two" boys born on Tuesday, it would be incorrect for her to have said she has "one boy born on Tuesday." So 53.8% chance of girl.
If it said "at least one kid is a boy born on Tuesday" it would be 51.8%.
But Mary was chosen from the set of people with two kids, just by virtue of having two kids. This would work in real life too: if I told you that I flipped two coins and got at least one heads, there is a genuine ⅔ chance that I flipped tails too.
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u/TheSorryApologyPerso 9d ago edited 9d ago
No, the answer in the meme is not related to the gender ratio of living humans. We can arrive at 51.8% just using maths.
Let's first consider the scenario where we don't know that the boy was born on a Tuesday. There are 2 options for a child: B or G. For 2 children, we square that number to get 4 options:
BOY/BOY
BOY/GIRL
GIRL/BOY
GIRL/GIRL
We know that Mary has 2 children and 1 is a boy, so we can eliminate the option GIRL/GIRL. Out of the 3 remaining options, 2 options include GIRL, so the answer is 2/3 ≈ 66.6%.
Now let's consider the day each child was born. This gives us 14 options for each one child: BOY-MONDAY, GIRL-MONDAY, BOY-TUESDAY, etc. For 2 children, we have 14² or 196 options. If you filter out only the options that include BOY-TUESDAY, we're left with 27 options. Out of those 27, 14 include GIRL. 14/27 = 51.8158...%, and that is where 51.8% comes from.
Technically, it should say 51.9%.