1- Sintetic: we see “family” as a whole system and we see 2/3 probability;

2- Analitic: we see an isolated event inside the system “family” and we see 1/2 probability.

If Jacob wanted to induce the sintetic approach, he could have asked:

“We have a large set of families with 3 kids, and 1 is male in all of them. In this set, what’s the probability of the existence of families with 2 brothers and one sister?”

In the second scenario, If sibling A is a girl. Sibling B CAN BE A BOY OR A GIRL. If sibling A is a boy, Sibling B is a girl. If Sibling A is a girl we don’t instantly know the gender of Sibling B. This means we have to add a probability. Where the was only once choice, we know have two. So it’s (1+1) + 1 possibilities. Two of which include a boy

]]>After you know the third person’s gender then you will be able to say what is as a percentage 2/3 male or female. But not before you know the gender of person 3. The unknown gender of person number 3 is not a math question, it’s a genetic outcome of a birth that the first 2 people have no influence on.

Older or younger siblings have no outcome as their gender has no influence of the outcome of the third persons gender.Each birth is a tossup as to it’s outcome.

If you think otherwise please explain how my brother or sister determined my gender. You can’t…

]]>There is mind games going on here Jacob as you say you are not going to say what gender they are then you say the gender of his sister. You are throwing confusion into a very simple equation and confuse the known genders and imply they predict the third outcome

The answer is that the chance that he has a brother is 50/ 50.

The 2/3 comes into play only in that you know the gender of 2 of the 3 people in question. He is a male, sister is a female.(this is the 2/3 that is answered in your explained equation.) But the known gender of these 2 people has no influence on the gender of person number 3. The third person can only be 1 of 2 things. it’s male or female, no other outcome can be made from the info given. So the answer to the question of the percentage of odds of this third person being male or female is 50/50. It can be no other answer. Try all you want to confuse people, the third person has a 50/50 chance of being one or the other.

]]>Are twins/triplets included in the probabilities? (Sorry, it’s too soon after lunch for me to calculate!)

]]>I am not going to reveal their gender

= they are sitting in two non-transparet boxes in front of us, box No.1 and box No.2

I will tell you that he has at least one sister

= we know that in one of the boxes a woman is placed

What is the probability that he also has a brother

= what is the probability that there is a man sitting in one of the boxes

Possibilities:

1W2M

1M2W

1W2W

Answer: 2/3

Question is would all agree with the translation?

]]>It’s easier for me to see the distinction if I look at the problem as drawing black and white marbles from a sack of equal numbered black and whites. One way to look at the problem is we draw bb bw wb (yes it is different since we draw one at a time) and ww. Now somebody says one is w. So we toss all bb draws back. This will give us the 2/3 outcome. Two possible draws out of 3 total.

But what if saying one is w means something like – draw a marble, it’s w btw. What is the probability the next will be a b? In tis case the w knowledge is just a statistic. And the answer to this question is 1/2…the intuitive 50-50.

Somehow the selection of the wording or the order or the implication that what appears to be a statistic is actually a constraint that forces us to toss bb back.

Look at the great response. People are thinking. Cool seeing everyone doesn’t answer the same way.

]]>You start with the population statistics (presuming it’s known, if not, the convention is to start with a uniform distribution). However, once you’re told more, you’re calculating P(X|new information+old information). This is Bayesian updating and people tend to be really bad about it for rare uncertain events. This is not even THAT problem.

I think most people who trip up fail to notice the “AT LEAST ONE” part. This is a statement about which parts of the total distribution are still valid outcomes.

]]>MMM

MMF

MFM

MFF

FMM (eliminated)

FMF (eliminated)

FFM (eliminated)

FFF (eliminated)

Now ONLY keep the remaining ones that have AT LEAST ONE FEMALE (that’s either 1 or 2 but not 0)

MMM (eliminated)

MMF

MFM

MFF

FMM (eliminated)

FMF (eliminated)

FFM (eliminated)

FFF (eliminated)

How many outcomes are left? 3

How many of those have a brother in them? 2

Answer: 2/3

]]>The problem changes after you say there is a sister. It’s a trick question in the sense that the number of total outcomes changes halfway through the problem.

The math would imply one or the other person is misguided because the real argument is are there three total outcomes or two. When are you supposed to start calculating probability, before Jacob tells you there is a sister or after?

Ironic how this was posted as seeing the unseen. Math can be blinding.

]]>The FFF was eliminated. All other possibilities have at least one M (the man).

]]>Please read all the post-comments above. It seems that everybody makes the same mistakes and they’ve been covered and explained multiple times already.

]]>We can´t know that.

Mikko is right.

Jacob´s reasoning is:

MMM (eliminated)

MMF

FMM

FMF

2/3(notice how M is always in the middle)

but he misses:

MFM

MFF

FFM

FFF (eliminated)

MMM (eliminated)

MMF

MFM

MFF

FMM

FMF

FFM

FFF (eliminated)

-Mikko

]]>“A man has two siblings. I am not going to reveal their gender, but I will tell you that he has at least one sister. What is the probability that he also has a brother?”

As I see it, these are the permutations for the three siblings:

MMM

MMF

MFF

FMM

FMF

FFF

After we eliminate MMM and FFF (“man” is a man, and one of his siblings is female), we are left with these possibilities:

MMF

MFF

FMM

FMF

So there’s an equal probability for two females or two males.

Am I missing something?

-Mikko

]]>I’m afraid I still don’t agree on that — the problem was as stated and it includes sufficient information to make the right conclusion, as well as the opportunity to make the wrong one (as I did initially, I admit…)

But more tongue-in-cheek though, I’d say that once we come to public policy decisions ALL problems are likely to be badly stated 😉

]]>