Monday evening puzzle

IanMunro, you deserve a

Just send me £20 for admin and p&p costs and it will be with you within 6-8 weeks.

Also have a look

Blue is boy, red is girl. All the outcomes that can’t be considered (eg: two girls, no boy born on a tuesday) are faded). This leaves 27 possibles. 13 of those are boy boy, so 13/27. Which is roughly 0.48.

flipping a coin, the probability of getting two heads in a row: 0.5 x 0.5 = 0.25. The first flip doesn’t affect the second but the overall probability is changed. the same goes with gender of successive children (assuming a 0.5 probability of either gender).

Ok try this…
I have 8 coins, i put each of them in pairs, one in each combination

1)HH
2)HT
3)TH
4)TT

I then show you a Head and ask you to guess which of the 4 combinations it is. What are your chances of geting it right?

what cvck says.
are you sure you’ve copied the Q correctly, realman?

you haven’t worded the original question that way

either that or I have misread it.

Isn’t
“What is the probability he has two sons?”
very differennt to
“what is the probability of 1an unkown child being male?”

Isn’t
“What is the probability he has two sons?”
very differennt to
“what is the probability of 1an unkown child being male?”

In all 3 questions you know the Man has 2 children, with at least one being male.

Therefore he can either have a son and a daughter, or two sons.

So asking does he have two sons, or asking is the other child male, are the same thing. I think..

CharlieMungus, I really like that explanation with the 8 coins.

The way that I read the first question was that we know he has a son. Therefore we have prior knowledge that one is a son so we only have to worry about the other child, the genders of the children being mutually exclusive made it into “A guy has a kid, is it male or female?”, so 50/50.

The question

“Mr Smith tells you he has 2 children. He introduces John, his son, to you. What is the probability he has another son”

is vastly different to

“Mr Smith tells you he has 2 children. What is the probability he has two sons?”

The way that I read the first question was that we know he has a son. Therefore we have prior knowledge that one is a son so we only have to worry about the other child, the genders of the children being mutually exclusive made it into “A guy has a kid, is it male or female?”, so 50/50.

Have a look at CMs explanation with the 8 coins above.

You are right, those two questions are different. I don’t see your point though.

Therefore he can either have a son and a daughter, or two sons

so 50-50 right?

I have a coin and I flip it, it can be Heads or Tails so 50/50 chance. I flip another coin, what are the chances of it being heads?

….I will mull it over dinner and a glass of wine.

Where’s my damn gold star, I worked it out without no steenking googles.

I have a coin and I flip it, it can be Heads or Tails so 50/50 chance. I flip it again, what are the chances of it being heads?

50/50. But that’s a different question.

You flip two coins. One of them is a head.

Given this information, what’s the possibility that you’ve got two heads?

Cougar, he got a gold star for effort. He listed every possibility lol.

You’re just one of those lazy clever people. No gold star for you. You just get that warm feeling from knowing you’re better then everyone else.

Ah, fudge, I missed that post; it was entered while I was typing mine up.

right, I think the 13/27 answer is bullsh!t, it may be mathematically correct, but it is irrelevant to any situation other than for willy-waving statisticians
you could introduce any kind of variable to the equation, like ‘one son was born at 4pm’ which would influence the probability, but it would be of no practical use to anyone to work it out

You flip two coins. One of them is a head.

Given this information, what’s the possibility that you’ve got two heads?

Ah ok, that’s a bit different to how I interpreted the question. I was answering

“You flip two coins. The first of them is a head. Given this information, what’s the possibility that you’ve got two heads?”

To be fair, that’s not what the first question says. It is what the -second- one says, however.

Cougar you can have the gold star on weekdays, if I can have it on weekends.

Yeah true, I’m now really confused. Fix where I’ve gone wrong here please!

P(boy given boy) = P(boy and boy) / P(boy)

so P(boy given boy) = P(0.25) / P(0.5)

so P(boy given boy) = 0.5?

right, I think the 13/27 answer is bullsh!t, it may be mathematically correct, but it is irrelevant to any situation other than for willy-waving statisticians

😀

Cougar you can have the gold star on weekdays, if I can have it on weekends.

Ok. When do you want the suspenders and high heels?

Yeah true, I’m now really confused. Fix where I’ve gone wrong here please!

P(boy given boy) = P(boy and boy) / P(boy)
so P(boy given boy) = P(0.25) / P(0.5)
so P(boy given boy) = 0.5?

Search me, I’ve slept since I was last in any sort of mathematical education.

To answer my own version of the question,

You flip two coins. One of them is a head.

Given this information, what’s the possibility that you’ve got two heads?

You could have a head and a tail, a tail and a head, or two heads. So probability is 1/3.

Retro-fitting this back to the original question,

You have two children. One of them is a boy.

Given this information, what’s the possibility that you’ve got two boys?

Yeah true, I’m now really confused. Fix where I’ve gone wrong here please!

P(boy given boy) = P(boy and boy) / P(boy)

so P(boy given boy) = P(0.25) / P(0.5)

so P(boy given boy) = 0.5?

chvck, p(a|b)=p(a.b)/p(b)

So the probability of boy boy given at least one boy should equal probability of boy boy and boy divided by probability of boy.. And then I get confused. Much easier to use the other method.

it may be mathematically correct, but it is irrelevant to any situation other than for willy-waving statisticians

Are you new to puzzles? They’re not supposed to be practical real-world problems. You’re unlikely to actually find a jailer who counts prisoners by adding rows of cells together, or people on an island sentenced to death unless they can say what colour hats they’re wearing.

Good grief.

Ian proper LOL to that video.

or people on an island sentenced to death unless they can say what colour hats they’re wearing.

Good grief.

😆

this isn’t a puzzle though, it’s a trick question designed to outwit those who haven’t studied statistical probability to a certain level.
if you haven’t studied it then you wouldn’t get to the answer of 13/27.

Last time I did maths was in 1990, and I hated statistics (largely for reasons like this).

its basically a big old troll I know but just read up on this ‘problem’ on wiki
wiki leads me to the opinion that the most intelligent among us are those who point to the ambiguity of the question 😉

I hated statistics (largely for reasons like this)

me too, 2 maths A-levels with as much pure maths and mechanics in as possible and as little statistics

the most intelligent among us are those who point to the ambiguity of the question

8)

it’s a trick question designed to outwit those who haven’t studied statistical probability to a certain level.

Or maybe its a question designed to make you think a bit more then usual? That’s what I aimed for, just to get people to think a bit. I knew most people would jump to conclusions and get it wrong, then eventually realise the right answer.

Its not always about getting the right answer, but quite often just about understanding why you were wrong at first.

Here’s a way of looking at it, that might help rationalise it.

“Out of everyone in the UK who has two children, one of which is a boy who was born on a Tuesday, what’s the probability that a couple picked at random has two sons?” Same question, pretty much, yeah?

Out of our pool, first we eliminate all the people who don’t have one or two sons (along with people who don’t have exactly two children and people who aren’t in the UK). This leaves us with the answer in our original premise – once we’ve knocked out the girls, our probability of getting two boys is one in three.

Now, we eliminate everyone who doesn’t have a son born on a Tuesday. Critically here, the people with two sons have two lottery tickets; they’ve got more chance of staying in our demographic than the people who only have one son, almost double in fact. This evens the odds quite considerably, as you can see in the answer to the Tuesday version of the puzzle – 13/27 is very nearly 1/2.

Regarding this Tuesday example, it’s relatively easy to work out the odds. The problem could easily have said “a boy who was ginger” or “a boy who likes apples” but the odds of that happening are less immediately obvious than “born on Tuesday”.

For any given filtering criteria with a probability of “1 in x”, the answer is going to be “2x-1 out of 4x-1” (I think – I’m making this up as I go along). With a 1-in-1 certainty (eg, if we were to say “…and the son is male”) the probability comes out at 1 in 3, which is what we had in the first place. As the criteria gets more specific, it tends towards 1 in 2. If instead of Tuesday we’d said “born on Christmas Day,” we’d have ended up with 729/1459, which is 1 in 2 to any sensible number of decimal places.

I think.

2 maths A-levels with as much pure maths and mechanics in as possible and as little statistics

Ditto, though I wouldn’t be as bold as to say I was hugely successful at them.

Its not always about getting the right answer, but quite often just about understanding why you were wrong at first.

it’s also about questioning/ challenging what someone else deems to be the correct answer… just because it can be ‘proven’ mathematically. 13/27 is the right answer according to one branch of mathematics.
–
for me, it’s frustrating because it is counter-intuitive

ambiguity of the question

+1

If you haven’t got that far then you are way behind.

Lol. Great to see this two year old thread still has plenty of legs. Good work RealMan.

Also, yes, the plane will take off. 🙂

If anyone’s still struggling with the original question, I just stumbled across this:

http://en.wikipedia.org/wiki/Boy_or_Girl_paradox

… one key point it makes here is the question wording is pretty critical.

I’m pretty sure the question(s) are worded OK 🙂

This is just the start of my 9 week module on probability and discrete mathematics, expect more of these..

….no please

This is all bullshit…

They all have 2 children, all of them already have 1 son, so the probability of them having 2 sons depends solely on the sex of the other child, which can only be 1/2, or 50%.

The way the question is worded, you may as well say what’s the probability of someone having a son, rather than a daughter.