Math Qustion

A woman is chosen at random among all women that have two children. She is asked if she has any boys, and she answers 'yes.' What is the probability her other child is a boy? Assume every pregnancy has a 50/50 chance to be a boy or a girl. Round your answer to 2 decimals.

This sounds real easy but then again i'm not sure...i need the answer before friday though....THANK YA!

~CaM~

1/3 rounded, it would be 0.33 in decimal form

The logic behind it:

If the woman has a 50/50 chance of having a boy or girl than there is four possibilities when having two children.

1. girl than boy
2. boy than girl
3. girl than girl
4. boy than boy

You know that 3 can not possibly be the answer because you know, for a fact, that she has at least one boy, thus she has a 1/3 possibility of having a another boy.

Kalika

.50? Right? If each kid has a 50/50 chance of being a boy, it wouldn't matter if the other sibling was a boy or not. Right?!? ACK!!! I dunno.

Bah, it's one third. Use your brain.

Kalika

kalika as confused as I am
you made sense lol

it should be a 100% considering that the question asks if she has ''boys'' thus indicating more than one...therefore if she only has two children she must have two boys...

It's a 50/50 chance the other child is the boy. There are two possibilites for what she'd have, boy or girl, Therefore it can't be one third because there are only two options. 'girl then boy' and 'boy then girl' can be put into one option. So you have either 'boy/girl', or 'boy/boy'.

There are four options, probability people.

1. boy came first than girl
2. girl came first than boy
3. two boys
4. two girls.

Since it can't be two girls, it's 1/3 chance. It's not that hard. honestly people, do you think they would really give her that question if the answer was 50/50.

If you go with 50/50, you will be wrong.

Kalika

haha it's blatently 50/50 because in the question it says assume that there is an even chance of having a boy or girl
it's like if i flip a coin 99 times and 50 times it is heads and 49 times it is tails then the probibility of getting heads still remains 50/50 it wont deffinitly be tails just because it would make it add up to 50
the past does not affect the future when it comes to probability!!

Okay, fine, don't believe me, but when your teacher tells you the answer, share the answer with the rest of us. I know I'm right because I had this question before when I was in school and I was the only person who got it right.

Kalika

OK Albatross (Kalika) is correct.
The question is asking for probability, and most of you are assuming and lumping boy then girl and girl then boy into one class. You must remember that this is mathmatics, and more importantly, probibility theory.

there are of course 4 groups:-
Boy Boy
Boy Girl
Girl Boy
Girl Girl

seen as the lady is asked if she has any boys and she answers yes, the girl girl option is not available.

this leaves 3 groups:-
boy boy
boy girl
girl boy

the question asks what is the probibility that she has boy boy to which the answer is 1/3 or 0.33 to 2 decimal places.

I would like to thank Albatross (Kalika) for being logical.

On a side note i am backing my knowledge up with my Diploma in higher mathematics, and my Degree.

i duno..cos she could have twins..and maby have a boy and a girl ..i duno lol

the question deos not ask if she has two boys it asks the probability of the other child being a boy which is 50% .50 1/2!!!!

Again i want to point out that you must think in probability theory!

There are 3 groups because although order doesnt matter, both boy girl and girl boy are still possible combinations.

EXAMPLE
If you are flipping 2 coins do you lump heads tails and tails heads together? Not in probibility theory you dont. You must consider ALL groups.

This is a probibilty question therefore you must think about it using probability theory and answer it by usings probability theory. Therefore there are 4 groups with a stipulation, leaving 3 groups.

Just because its a 50/50 chance of having a boy or girl you must consider that there are other factors to the question. remember that this woman MUST have answered yes to the question "do you have any boys" and although order doesnt matter this woman could have had a boy then a girl or a girl then a boy. which is 2 SEPARATE options of probability.

EXAMPLE
if the question was changed slightly and it asked if the second child was a girl, would you still be arguing the case for lumping boy girl and girl boy into the same category?

And aaron, it does ask if she has two boys. she is asked "do you have any boys?" she answers "yes" so she must have at least one boy. then the question is posed "what is the probibilty that the OTHER child is a boy?" therefore it is simply asking what is the probability of having boy boy or two boys.

I will attempt to simplify the question.

What is the probability of boy boy using the following groups?

Boy Boy
Boy Girl
Girl Boy
Girl Girl

obviously 1 in 4

ok so now i add a stipulation that the person asked must have at least 1 boy.

this obviously removes the girl girl gorup as a possible outcome. leaving 3 groups

Boy Boy
Boy Girl
Girl Boy

so what is the probibility of boy boy?

1 in 3

I would like to thank Albatross (Kalika), and google for proving to the world that just because the many say the same thing, it doesnt mean they are correct.

I think Albatross (Kalika) deserves all the credit for this one. well done.

k thanks i'll chose .33....i'll be gettin the answer monday so i'll post it then and how to get the answer...thank ya!
~Cam~

dd uno its nt 50/50. chances of havin a girl r actually slightly higher then havin a boy. i duno y, i learnt it in science

but in the question it says presume that the chances are 50/50

anyway if that is true i still dont understand it i mean i understand about the groups and how they work but i dont get how that makes a difference i mean if the chance of her having a boy or a girl is 50% then surely it wouldn't matter what the other baby is? please someone explain it better for me!!!

Hey, whats the answer?! :)

i think you missed the point of the question it was more of a thought experiment probability thing rather than an actual question on boy to girl birth rate question

Thank you C. Fowler. I'm so glad someone agrees with me. Much appreciated.

Probability theory, it's what I have been preaching!!!

Really, what makes the question confusing is poor wording. It just takes a little less linear thinking to figure it out. Thanks for googling it, however, Hopefully that will help change some minds.

Kalika

kalika can you explain it to me please because i still don't get it i still think it's 50/50

btw who was right?

what other gender is there? its either a girl or a boy.... so thats 50/50.. it doesnt matter what the other one is...duhh...sheeshhh.. trick question much?

I'm Horrible With Math...Sorry xoxo-Nikki-xoxo

CONGRATULATIONS TO Albatross AND EVERYBODY ELSE WHO AGREED WITH HIM!!! The answer was 0.33 and Albatross was absolutely right about how 2 get it. :)

The reason for this question is that i want to open a math contest in which the prize is ur poems poems being read...for more info about da contest read the topic Math Contest- Week #1.

Thank you for all of your participation and I hope that as many peolple that answered in this one willa answer throughout the whole contest! =]

~CaM~

Are you sure? I mean, if there's a 50/50 chance every pregnancy results in a boy, wouldn't there be a 50/50 chance her other child is a boy?

Awesome, Thanks.

Oh, and by the way, I'm a girl. ;)

Kalika

Ok jamie... think of it this way

The lady is not pregnant. we are not trying to figure out if her unborn child is male or female. what we are trying to figure out are the different probabilities of having different combinations of children. for example girl then girl, girl then boy, boy then girl and boy then boy.

Again i must sttress that you must answer the question using probability theory.

On a side note i want to say to apathetic soul that the question specifically states that the woman is taken from a group containing women who have had 2 children... therefore we know for certain that she has 2 children and not 3 or 4. Also the question is specific about the odds of having different children... 50/50 location has no say in this question, and plays no part in the probability theory of it.

All right, I think I get it. Thank you C.