1701

right. Giving this a try.

I’m gonna give you a problem.

“There’s three types of ways a 2 child family can include boys. The Smith family is one such family. What is the probability that the Smiths are type A?”

This problem is simple to solve. Three types of ways, you’re looking for type A, so that’s one third. Note the problem is really limited. No mention of quantity of boys, etc. Just “types of ways”.

This is what the original problem is really asking you, under the riddly language.

1702

JESUS MOTHERFUCKING CHRIST, MY BOSS JUST ASKED ME A HARDER VARIANT OF THIS QUESTION AND NOW I SEE THAT THIS THREAD HAS BEEN NECROED WITH 1,682 FUCKING POSTS?!?!?!?!

In the ORIGINAL goddamned post, the answer is 1/3.

Now, here’s the one my friggin’ boss asked me. This was probably already posted but I’m sure as shit not going to read 57 pages of this idiocy.

“You meet a man. He says he has two children. One of them is a boy, born on a Tuesday. What are the chances the other one is also a boy?”

It turns out the answer is 13/27. And HERE IS MOTHERFUCKING WHY.

Look at all the original possibilities for a two-child family. There are two kids, each of which may be a boy or a girl, and each of which may have been born on any of the seven days of the week. Let’s lay out the possible families (in order eldest-youngest):

  • 49 possible boy-boy families.
  • 49 possible boy-girl families.
  • 49 possible girl-boy families.
  • 49 possible girl-girl families.

Now, we can eliminate all the girl-girl families, because we know he has one boy child. So here are the remaining possible families:

  • 49 possible boy-boy families.
  • 49 possible boy-girl families.
  • 49 possible girl-boy families.

(Note that if we leave out the “Tuesday” part, then these are all equivalent, and the odds that his other child is a boy are 1/3, that being the answer to the original question.)

Now, out of these families, how many of them have a boy born on Tuesday?

  • There are 7 girl-boy families where the boy was born on Tuesday.
  • There are 7 boy-girl families where the boy was born on Tuesday.
  • There are 13 boy-boy families where AT LEAST ONE OF the boys was born on a Tuesday. (In seven of them, the eldest was born on a Tuesday; in six more, the youngest (but NOT the eldest) was born on a Tuesday.)

This totals to 27 families. In 13 of them, the other child is another boy.

Therefore, the answer is 13/27.

(My boss points out that he is not a Bayesian. I’m not either, because if I were, I could understand this much better:

Then I could teach robots to drive cars too, which is something that everyone who can’t be convinced that the original answer is 1/3 will never be able to do. I got the simple version wrong initially as well, btw, but at least I figured out the right answer with only two nudges…)

1703

Yes. Perhaps you should have looked at the last couple of pages, discussing your variant.

In the ORIGINAL goddamned post, the answer is 1/3.

There is little hope for you.

“You meet a man. He says he has two children. One of them is a boy, born on a Tuesday. What are the chances the other one is also a boy?”

It turns out the answer is 13/27. And HERE IS MOTHERFUCKING WHY.

The answer is not (generally) 13/27. You can find out why in, well, this thread, or you could read, for example, this post.

1704

Why did you start trolling?

1705

At this point, just let a few dingoes loose in the neighborhood. Probability will steadily approach zero.

1706

Right.

Now… I think that this same issue applies in the coin flip problem. TH, HT, and HH are the only three possibilities when two coins are flipped and you know that at least one is heads.

Etc.

1707

What the fuck?!

I need a T-shirt that says “I may not be Skedastic, but Skedastic is totally fucked up.”

1708

I think the issue is with the phrasing of the question. It states that one is a boy, born on a Tuesday, but that does not mean that both boys cannot be born on a Tuesday. Shouldn’t it be 14 boy-boy families where at least one is born on a Tuesday?

7 cases where the oldest is born on Tuesday
6 cases where the youngest is born on Tuesday (but not the eldest)
1 case where the youngest is born on a Tuesday (and the eldest as well)

Which equals 14/28, or 1/2.

The 13/27 answer discounts both boys born on Tuesday by artificially inserting an “oldest not born on Tuesday” case. That’s like saying “if the youngest is not born on Tuesday, than the oldest must be, so there are only 6 cases where the oldest is born on Tuesday”.

1709

I still want to know why Mr Smith gets off on the 35th floor at the end of the day.

1710

That article does a good job explaining why is it not 13/27.

1711

You’re over counting. There are 14 possible cases which include the older boy born on Tuesday. One of those cases is where the younger boy is also born on Tuesday. Of these 14 cases, 7 of them include another boy.

Now that we’ve counted all the cases where the older boy was born on Tuesday, we count cases where the older boy was not born on Tuesday (which implies that the younger boy was born on Tuesday ). There are 7 cases here where the oldest child is a girl. There are 6 cases where the oldest is a boy, one for every day except Tuesday.

1712

He’s a midget, but when it rains he uses his umbrella.

1713

What these puzzles show is that it is quite difficult to state a probability problem with an unintuitive answer in ordinary English so that the unintuitive answer is unambiguously correct. This is because English evolved to handle realistic situations, where very likely intuitive answers are correct. No one is actually going to say “at least one is a boy”. They might say something like “My son John likes to play baseball.” You might assume this conveys the same information as “at least one is a boy,” but from the actual wording, you’d be likely to assume that the second child is a girl-- because otherwise he’d have said something like “My elder son John likes to play baseball,” or he would have said John with sufficient emphasis that you knew there was another son. Your intuition takes into account cues like this; it also takes into account simple observational biases like the one that confounds the “unintuitive” answer to the original “boy in the window” problem.

The “Tuesday” variant is a good example of the absurdity of trying to make ordinary English convey this kind of probability problem with precision. To get the “13/27” answer, you have to interpret the statement “I have a son who was born on Tuesday” as conveying the information “Of all possible combinations of my children’s birthdays and days of the week, you should only consider the cases where a male child was born to me on Tuesday.” And really, that’s not what it would mean in any remotely realistic scenario.

1714

I <3 antlers.

1715

What if the boy is on a treadmill?

1716

Ah, I see now, it’s because the Tuesday-Tuesday case cannot be counted twice.

I was considering each case separately: if you surmise that the Older was born on Tuesday, you get 7 day possibilities for the younger; if you surmise that the Younger was born on Tuesday, you get 7 day possibilities for the older.

Instead, I should’ve just counted Younger boy birth day possibilities given the birth day of the Older, given that at least one must be born on a Tuesday.

Older birth day --> Younger possibilities:
Mon --> 1 possibility for the Younger (Tues)
Tues --> 7 possibilities for the Younger (any day)
Wed --> 1 (Tues)
Thurs --> 1 (Tues)
Fri --> 1 (Tues)
Sat --> 1 (Tues)
Sun --> 1 (Tues)

1 + 7 + 1 + 1 + 1 + 1 + 1 = 13

1717

He takes off, and I shoot him in the goddamned head for being ambiguous.

1718

He’s got a 50% chance you’ll miss!

1719

How much airspeed velocity does he gain from the headshot?

1720

Fucking riddles, how do they work?