# When intuition and math probably look wrong

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When intuition and math probably look wrong

This brings to mind the sort of advanced thinking that tourney pros may contemplate

when sizing their next bet. It also reminds me of the Monte Hall proposition in 21. zg

………..

When intuition and math probably look wrongsciencenews.org

I have two children, one of whom is a son born on a Tuesday.What is the probability that I have two boys?

Gary Foshee, a puzzle designer from Issaquah, Wash., posed this puzzle during his talk this past March at Gathering 4 Gardner, a convention of mathematicians, magicians and puzzle enthusiasts held biannually in Atlanta. The convention is inspired by Martin Gardner, the recreational mathematician, expositor and philosopher who died May 22 at age 95. Foshee’s riddle is a beautiful example of the kind of simple, surprising and sometimes controversial bits of mathematics that Gardner prized and shared with others.

“The first thing you think is ‘What has Tuesday got to do with it?’” said Foshee after posing his problem during his talk. “Well, it has everything to do with it.”

Even in that mathematician-filled audience, people laughed and shook their heads in astonishment.

When mathematician Keith Devlin of Stanford University later heard about the puzzle, he too initially thought the information about Tuesday should be irrelevant. But hearing that its provenance was the Gathering 4 Gardner conference, he studied it more carefully. He started first by recalling a simpler version of the question called the Two Children Problem, which Gardner himself posed in a Scientific American column in 1959. It leaves out the information about Tuesday entirely: Suppose that Mr. Smith has two children, at least one of whom is a son. What is the probability both children are boys?

MORE- https://www.sciencenews.org/article/when-intuition-and-math-probably-look-wrong

Intuition and math don’t look wrong.

ZG,

If you read through the comments, you’ll realize that the intuition that there’s a 50% probability of the other child being the boy is actually

correct. The article was mistaken. Here are the true possibilities of the second child being a boy, given that one of the children is a boy (credit from the comments):”

First, let’s assume birth order does NOT matter, here are the possibilities for the gender of a child:

1) Boy

2) Girl

so 50% chance of Boy.

If we assume birth order matters, then these are the possible combinations:

1) Boy(known), Boy

2) Boy(known), Girl

3) Boy, Boy(known)

4) Girl, Boy(known)

Still 50% chance of Boy.

”

The article tried to present the answer of 1/3 (33%), which wasn’t correct.

The article tried to present the answer of 1/3 (33%), which wasn’t correct.

You need to go back and carefully STUDY the article. It presents the answer of 13/27, which is ABSOLUTELY correct.

Sucker,

I was referring to the simpler problem given in the article. I studied the article a bit more, and I still stand by what I said. I will explain myself fully, and please feel free to point out the problem in my logic.

*********************

I will use 3 names in my reasoning: John, Matt, Sally.

The problem is that the article doesn’t take into account that we are “given” that John was born on Tuesday. That is the assumption upfront. We already have John born on Tuesday. We also know that John has a sibling. The article also doesn’t take into account that the order in which they are born is

notimportant. So here are my possibilities,giventhat John is born on a Tuesday:1. John: Tuesday, Matt: Sunday

…

7. John: Tuesday, Matt: Saturday

8. John: Tuesday, Sally: Sunday

…

14. John: Tuesday, Sally: Saturday.

That is 14 possibilities, of which 7 of them have a male sibling (Matt), and 7 of them have a female sibling (Sally). Hence 50%.

*******************

Now, regarding the article’s logic.

If you look at their chart http://www.sciencenews.org/view/download/id/60731/name/WORKING_IT_OUT (Link is dead) you can see that they would consider John and Sally both born on Tuesday as separate events that should be counted twice towards the total. Because their logic is that if John is younger, that’s 1 event, and if Sally is younger, that’s another event. In that case, yes, their reasoning is correct. However, nowhere in the original problem implies that John and Sally both being born on Tuesday should be separate events, because “what if John is younger, or what if Sally is younger” should imply counting the situation of both John and Sally being born on a Tuesday twice. That is where they are incorrect.

It’s a problem of English. What’s confusing is that it is unclear if the “one” used in the sentence represents the number 1, or what Germans would say as “

man” – “One eats breakfast in the morning and dinner at night,”und so wieder.In the second sense of the word, there is an increased probability that the second child is also a son born on Tuesday, because of the nonzero and non-excluded chance his children are identical twins. Barring that, and using this non-exclusive sense of the word “one” the other child is equally likely to be male or female or born on any day of the week.

Ungenau. I thought the same and gave no more thought to the question. There simply is no reason to attempt to devine the meaning of an imprecise question. Before you answer a question, you must understand it. It sometimes pisses off people that e-mail me questions when my response is more questions. But, precision is important. Otherwise, there can be multiple answers to a question, all conflicting and yet all arguably correct. Just not correct for the person asking the question.

My intuition says some of this German looks wrong.

ZG,

If you read through the comments, you’ll realize that the intuition that there’s a 50% probability of the other child being the boy is actually

correct. The article was mistaken. Here are the true possibilities of the second child being a boy, given that one of the children is a boy (credit from the comments):”

First, let’s assume birth order does NOT matter, here are the possibilities for the gender of a child:

1) Boy

2) Girl

so 50% chance of Boy.

If we assume birth order matters, then these are the possible combinations:

1) Boy(known), Boy

2) Boy(known), Girl

3) Boy, Boy(known)

4) Girl, Boy(known)

Still 50% chance of Boy.

”

The article tried to present the answer of 1/3 (33%), which wasn’t correct.

You’re not setting this up correctly –

For THIS problem, there are exactly THREE possibilities, all of which will occur with equal frequency:

1) The first child is a boy, second child is a girl.

2) The first child is a girl, the second child is a boy.

3) Both children are boys.

It’s quite clear from this that the chance of two boys can ONLY be 1/3.

Sucker,

I was referring to the simpler problem given in the article. I studied the article a bit more, and I still stand by what I said. I will explain myself fully, and please feel free to point out the problem in my logic.

*********************

I will use 3 names in my reasoning: John, Matt, Sally.

The problem is that the article doesn’t take into account that we are “given” that John was born on Tuesday. That is the assumption upfront. We already have John born on Tuesday. We also know that John has a sibling. The article also doesn’t take into account that the order in which they are born is

notimportant. So here are my possibilities,giventhat John is born on a Tuesday:1. John: Tuesday, Matt: Sunday

…

7. John: Tuesday, Matt: Saturday

8. John: Tuesday, Sally: Sunday

…

14. John: Tuesday, Sally: Saturday.

That is 14 possibilities, of which 7 of them have a male sibling (Matt), and 7 of them have a female sibling (Sally). Hence 50%.

*******************

Now, regarding the article’s logic.

If you look at their chart http://www.sciencenews.org/view/download/id/60731/name/WORKING_IT_OUT (Link is dead) you can see that they would consider John and Sally both born on Tuesday as separate events that should be counted twice towards the total. Because their logic is that if John is younger, that’s 1 event, and if Sally is younger, that’s another event. In that case, yes, their reasoning is correct. However, nowhere in the original problem implies that John and Sally both being born on Tuesday should be separate events, because “what if John is younger, or what if Sally is younger” should imply counting the situation of both John and Sally being born on a Tuesday twice. That is where they are incorrect.

The article does NOT state that John was born on a Tuesday. It says ONE boy was born on Tuesday; so you have to also include the possibility that it was Matt who was born on Tuesday.

There are 27 equal possibilities, of which only 13 consists of two boys:

John: Tuesday

Matt: Sunday

John: Tuesday

Matt: Monday

John: Tuesday

Matt: Tuesday

John: Tuesday

Matt: Wednesday

John: Tuesday

Matt: Thursday

John: Tuesday

Matt: Friday

John: Tuesday

Matt: Saturday

********

Matt: Tuesday

John: Sunday

Matt: Tuesday

John: Monday

Matt: Tuesday

John: Wednesday

Matt: Tuesday

John: Thursday

Matt: Tuesday

John: Friday

Matt: Tuesday

John: Saturday

********

Sally: Sunday

John: Tuesday

Sally: Monday

John: Tuesday

Sally: Tuesday

John: Tuesday

Sally: Wednesday

John: Tuesday

Sally: Thursday

John: Tuesday

Sally: Friday

John: Tuesday

Sally: Saturday

John: Tuesday

********

Sally: Sunday

Matt: Tuesday

Sally: Monday

Matt: Tuesday

Sally: Tuesday

Matt: Tuesday

Sally: Wednesday

Matt: Tuesday

Sally: Thursday

Matt: Tuesday

Sally: Friday

Matt: Tuesday

Sally: Saturday

Matt: Tuesday

Note that the reason that there are only 27 possibilities rather than 28, is the fact that if both boys were born on Tuesday, you can only count that ONCE, rather than twice.

So this article did INDEED give the correct answer to BOTH problems;

1/3 for the Two Child Problem, and 13/27 for the second problem. As it turns out, all those mathematical geniuses are right after ALL!

If you’re still having problems understanding this problem, I would suggest that you “Google” and study a similar problem; the “Monty Hall paradox”, which involves the same principles, only much simpler to understand.

You’re not setting this up correctly –

For THIS problem, there are exactly THREE possibilities, all of which will occur with equal frequency:

1) The first child is a boy, second child is a girl.

2) The first child is a girl, the second child is a boy.

3) Both children are boys.

It’s quite clear from this that the chance of two boys can ONLY be 1/3.

Why does order matter when it is boy/girl and not matter when it is boy boy? It seems to me there are FOUR possibilities:

1) The first child is a boy, second child is a girl.

2) The first child is a girl, the second child is a boy.

3) The first child is the known boy, second child is a boy.

4) The first child a boy, second child is the known boy.

I Win I Win

I chose not to answer because I would have seeeemed stupid

happy babies

I Knew It, All of You Are Pseudo AP’s

A real AP does not have children.

He eats them!

No Taco Bell