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Question about conditional probability (Possibly as interesting as the Monty-Hall Question)
Posted by: Todd's keyboard
Date: December 03, 2019 09:29AM
You find out a family has exactly two children and one of the children is a boy. What is the probability that the other child is also a boy?

(The assumption is that gender is a binary situation. Children are either boys or girls.)

Also, how would you explain this so it is clear to someone else?

Todd's still-trying-to-wrap-his-keys-around-this board
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Re: Question about conditional probability (Possibly as interesting as the Monty-Hall Question)
Posted by: decay
Date: December 03, 2019 09:40AM
51% chance it's a boy.

[www.npr.org]



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Re: Question about conditional probability (Possibly as interesting as the Monty-Hall Question)
Posted by: JoeH
Date: December 03, 2019 09:41AM
There would have to be additional information provided to turn this into a conditional probability question. Otherwise it is an independent probability for each child. The actual statistic is something like 51% of children born are male, but thought questions like this often assume a 50-50 ratio.
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Re: Question about conditional probability (Possibly as interesting as the Monty-Hall Question)
Posted by: wolfcry911
Date: December 03, 2019 09:51AM
1 in 3
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Re: Question about conditional probability (Possibly as interesting as the Monty-Hall Question)
Posted by: Todd's keyboard
Date: December 03, 2019 10:30AM
Thought about stipulating that one assumes an equally likely chance of boys or girls as independent events (to eliminate the slightly higher odds of boys being born). Please add that assumption (equally likely chance of having a boy or a girl as an independent event).

Quote
JoeH
There would have to be additional information provided to turn this into a conditional probability question.

What additional information?

How about adding a day of the week as additional information? Please assume that the same family lets it be known that it has one son who was born on a Tuesday. (Assume also that births are distributed evenly throughout the week, even though hospitals may show an actual tendency to try to avoid weekend births.)

Todd's still-trying-to-come-up-with-an-appropriate-analogy keyboard
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Re: Question about conditional probability (Possibly as interesting as the Monty-Hall Question)
Posted by: TLB
Date: December 03, 2019 11:56AM
Does birth order matter? If so, B-G <> G-B.









j/k
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Re: Question about conditional probability (Possibly as interesting as the Monty-Hall Question)
Posted by: Todd's keyboard
Date: December 03, 2019 01:07PM
Quote
TLB
Does birth order matter? If so, B-G <> G-B.
j/k

In this scenario, birth order does not matter. More precisely, we don't know if the one known son is the oldest or youngest.

T's kb
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Re: Question about conditional probability (Possibly as interesting as the Monty-Hall Question)
Posted by: neophyte
Date: December 03, 2019 01:39PM
100%






Both children are adopted, and the parents adopt only male children.
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Re: Question about conditional probability (Possibly as interesting as the Monty-Hall Question)
Posted by: Todd's keyboard
Date: December 03, 2019 02:09PM
Is this the same question—although replacing black and white go stones for children?

An urn has four go stones, two white and two black. Someone has randomly picked two of the stones. That person reveals to you that one of the stones is black. You don't know if it was the first or second pick. (A reminder: The picks have already been made.)

What are the odds that the person has a second black stone?

Todd's not-sure-if-the-analogy-holds keyboard
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Re: Question about conditional probability (Possibly as interesting as the Monty-Hall Question)
Posted by: Filliam H. Muffman
Date: December 03, 2019 03:16PM
I was one of three boys. My dad's sister had five boys. My mom's brother's wife had three girls.

I would guess having one means the probability is higher to have the same, but I don't know where to look for typical statistics.



In tha 360. MRF User Map
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Re: Question about conditional probability (Possibly as interesting as the Monty-Hall Question)
Posted by: Harbourmaster
Date: December 03, 2019 06:54PM
Do both children have the same pair of parents?



Aloha, Ken


“I have developed significant attachments to several members even though I wouldn't recognize them if I sat next to one on a park bench. I'm often tempted when in an airport to walk around, hollering "The Løpe", to see if anyone other than the Homeland Security people will acknowledge me. ” - The Løpe
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Re: Question about conditional probability (Possibly as interesting as the Monty-Hall Question)
Posted by: Sarcany
Date: December 03, 2019 07:36PM
Not enough info.

How many kids and of what genders did the male parent's dad, grand-dad and great grand-dad have?

[www.sciencedaily.com]



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Re: Question about conditional probability (Possibly as interesting as the Monty-Hall Question)
Posted by: rich in distress
Date: December 03, 2019 09:23PM




• back to confinement


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Re: Question about conditional probability (Possibly as interesting as the Monty-Hall Question)
Posted by: pdq
Date: December 05, 2019 09:24AM
Odd, but I’m pretty sure that as written, the chances are indeed 1 in 3.

With just the knowledge that one is a boy (not the first one, or the second one), that results in three possibilities: girl then boy - boy then girl - boy then boy.

...of which, only one has a second boy. So, one in three.

If you change this (what seems like) ever so slightly to “a couple has a boy. What’s the chance the next one is a boy?” then of course, it’s 50%.

I’ve heard this same paradox described this way: you have two cards - one is white on both sides, one has a white side and a black side. You pick a card at random and put it down on the table, and it’s white on top. What’s the chance it’s black on the other side?

Again, 1 in 3. How can that be? Because, of the 4 possible sides you could view in the first step, you’ve eliminated one by the description - it’s not black. So, there are three remaining possible sides to see, and only one has black on the other side.

Conditional probability.
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Re: Question about conditional probability (Possibly as interesting as the Monty-Hall Question)
Posted by: Todd's keyboard
Date: December 06, 2019 03:26AM
pdq has it correctly across the board. The birth order of the child is NOT stipulated and the odds of the other child being a boy is 1:3.

Saying the same thing in a slightly different way, there are four possibilities for a family to have two children. The below list of four children does list them in birth order, but birth order is not included in the question. If birth order were included in the question, the result would be different.

BB
BG
GB
GG

The fourth option (GG) is ruled out. (The family has at least one boy.) That leaves just one chance out of the three remaining possibilities that the second child (again, not in terms of birth order) is a boy.

What's even more amazing to me is a similar question with two conditions, gender of one child and day of the week that the same child was born.

A family with two children has a boy that was born on a Tuesday. (Again, we don't know if the boy is a first-born or second-born.) With the additional information of the day of the week, what are the odds the other child is a boy? (This assumes that there is an equal chance of babies being born on any of the seven days of the week.)

The answer is more than 1:3 and less than 1:2.

Todd's still-trying-to-figure-out-the-math-on-that-one-without-plotting-all-196-possibilities calculator
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