The Boy or Girl Probability Paradox Resolved | It was never really a paradox

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[zachstar]

Alright hopefully this video helps put this all together! As mentioned by wikipedia it was very hard to see why my initial assumptions were wrong. But thank you to everyone in the last video for the discussion about what is really going on within this problem.


Also I don't really talk about the 'born on a Tuesday' part in this video but the same math I talked about would apply (asking would yield a change, whereas someone just mentioning it would keep the probability at 50%).

[kokopelli]

As a side note, DON'T go to bars and start asking guys about their daughters, while putting money down.

[JimmyJJJohnson]

Just don't go into a bars full of statisticians when you make these bets. Only the ones with two daughters will take you up on the bet and you'll be wondering why you're having such a bad run of luck 😂

[albasuna]

The semantics of probability problems has cost me a great deal of letter grades.

[CarlSmithNZ]

The way I made sense of it in my head is this:
When he's talking about his "2 kids, one of whom is a girl", the "one" in question could be one of 2 people if he has two girls. As soon as he says the girl's name, or sees her and says "there she is", he's definitely talking about one specific girl. So the shift comes from a subtle change in meaning of the word "one": It changes from "either of my daughters if I have two daughters, or my only daughter if I have one of each" to "this specific daughter".

To me, this explains the "paradox", and I guess it kind of corresponds nicely to this video's explanation that half the time he'd say "Julie", and half the time he'd mention the "other daughter".



Great video though, it really helped me to start thinking about the paradox in the right way, since I've been aware of the puzzle for a long time and never really felt I'd made proper sense of it.

[juliemaricic-detweiler]

Of the few times I've heard my name in any form of media, this is by far the coolest.

[danielkunigan]

Oh thank goodness. My visceral anger is gone now. This sits right in my brain.

[danielcopeland]

Actually if the sentence they utter is "I have a daughter, " there is roughly a 0% chance they have two daughters, because if they had two daughters they would say "I have two daughters." That's how actual people talk.

[beng]

Outstanding! I knew the comments on your first video would be heated.. But this video explains the subtle details better than any I've seen. Well done!

[thenmiziz]

Well done! You nailed it.
There is so much shallow misinformation about this and related problems. Might be typical for the internet, but strangely enough even some math professors got this one plain wrong. (as was the case for the Monty Hall)
I was going to write you to clarify, but writing is hard and now you already did it in a very nice way.


Note 1: As a physicist, I like to think about it this way:
"asking people to step forward" is a preparation of a "state" or "ensemble" i.e. a set of possibilities
"asking (specific) questions" is a measurement on such a set.
If a problem is given in natural language, we always have to clarify which part is a preparation and which is a measurement!


Note 2: I only noticed one misspeak at 10:12 in this video.
You should have said: "If you --outright-- ask if they have a daughter named X, and you guessed correct, you get 50%"
If you first ask for "having a daughter" and later guess the name, the 33% still stand.
So, again no "jump" in probabilities!

[annoloki]

Okay, so if somebody tells you "No, Luke, I am your father", what are the odds that you have a sister?

[mbennettideaengcom]

Thank you for making these two videos. I saw the first one before my time in the back of an Uber today, and I admit YOUR first part popped into my mind, and I was so happy to see the second part when I got home today. Critical and detailed thinking skills, well, our civilization needs all the practice we can get! And a friendly style with some humor is one of the least threatening ways to go about it. Rock on!!! Oh, and hello from the Bay Area!

[tracyh]

Zach looks so happy in this video that he's finally resolved the paradox and the curse has been lifted.

[zilvarro]

"I have two daughters one of which is a girl whose name is Tuesday."

[narudavidkun]

Great video, the way you get the information changes everything.

[thedylman]

Random Guy: "Yeah, so my daughter Julie..."
Me: "UGHHH great, thanks a lot! Now I have to go back to a room with 10, 000 dads!"

[ashesashes]

Perfect this makes so much sense now! Thank you for this upload!

[MarcusCactus]

Simple foolproof test:
Does the fashion in which you got the information make a difference between boys and girls?
If the info is delivered randomly, no. So it must be 50%.
If you asked specifically for ‘girl’, yes. The prob can be different.

[buttonasas]

By nature of language and implying context, "I have two kids, one is a girl" means the other is a boy 99% of the time :D

[hunterk]

Yay, I had a correct explanation for the phrasing error in the previous video!