345 replies to this topic

[skale]

The answer is 25%. Before they had children the probability for a girl first is 50%. The probability for a girl second is 50%. BUT, to have 2 girls the probability moves to half of half, or 25%.

You might be on the right track but thats not the correct answer.

[unreality]

imtcb, you have fallen into something known as "gambler's fallacy"...

once a first girl is born, THAT DOES NOT CHANGE THE PROBABILITY OF ANOTHER GIRL BEING BORN.

Yes if you look at the whole thing total, it's 25% for two children to be girls

But we're looking at the next child only... and the fact that a girl was born already does not change the 50/50 probability.

One single coin flip is ALWAYS 50/50 (assuming the coin is standard and all that). It doesnt matter what has come before it- will be 50/50 always. But if you're looking at things as a whole, for example if I flip a coin three times the chances of three heads is 1/2 * 1/2 * 1/2 = 1/8. But that doesnt change the fact that the next coin I flip will either be heads or tails, 50/50.


so if we're just looking at whether the next child is a boy or girl, its 1/2 each.

[skale]

imtcb, you have fallen into something known as "gambler's fallacy"...

once a first girl is born, THAT DOES NOT CHANGE THE PROBABILITY OF ANOTHER GIRL BEING BORN.

That is correct BUT,

so if we're just looking at whether the next child is a boy or girl, its 1/2 each.

knowing one of the 2 kids is a girl does alter something else, now am giving away too many hints.. it gives you useful information!

[mdsl]

knowing one of the 2 kids is a girl does alter something else, now am giving away too many hints.. it gives you useful information!

It's 1/2 using conditional probability, so why don't you share your answer already so we can pick it apart.

[Riddari]

Spoiler for solution

The probability of both children being girls when we know at least one is a girl is 33%.

The normal possibilities for a set of two children are:
Boy/Boy
Boy/Girl
Girl/Boy
Girl/Girl

Since we know one of the children is a girl, we can drop the Boy/Boy possibility.
This leaves only three possibilities, one of which is two girls.

[skale]

Spoiler for solution

The probability of both children being girls when we know at least one is a girl is (1/3) - 33.33%.

The normal possibilities for a set of two children are:
Boy/Boy
Boy/Girl
Girl/Boy
Girl/Girl

Since we know one of the children is a girl, we can drop the Boy/Boy possibility.
This leaves only three possibilities, one of which is two girls.

That sum's it all.. good job Riddari!

[unreality]

ah so we are looking at the thing as a whole... good job riddari!

[comperr]

imtcb - they are imdapendant events: the answer is 1/2

[Garrek99]

If these are the possible combinations and you eliminated the boy-boy combo that means that you are solving this combo problem backwards. What I am trying to say is that since the untouched chances are 50% 50% because:
1st child / 2nd child
Girl / Girl
Girl / Boy
Boy / Girl
Boy / Boy
so for 2nd child the set of possibilities is {girl, boy, girl, boy} which gives 2 out of 4 for girls and gives you 50%.
YOU HAVE TO eliminate the 1st child boy, 2nd child girl because the 1st child is already known to be a girl.

THEREFORE: your only possible outcomes are girl girl and girl boy which gives you 50% 50%.

There is a puzzle about eliminating doors behind which prizes are hidden. I think it is "the price is right" puzzle; where a bit of knowledge helps you increase your chances of picking the right door with the prize but the puzzle you presented isn't it.

[comperr]

the point is:
if whether you had a boy or girl fist does not affect what you have later

the choices therefore are
?/boy(50%)
?/girl (50%)