Probabilities

[bednobs]

following on from the question the other day regarding russian roulette which i found fascinating, can anyone tell me the probability if you had 2 children of having a boy and a girl. Does the probability change, of say you had 5 boys already of your next one being a girl (taking out condsiderations such as things that are said to alter the by/girl ration globally and assuming there is always a 50% chance of either)
my common sense tells .me that it's always 50% of having a boy or a girl next, even if you've had 5 boys already, but my common sense isn't always that sensible

[Prudie]

Mathematically it's 50% but that assumes they are equally likely (like picking a ball out of a bag of two) but i think genetics,diet, time of conception and all sorts of other things can influence sex of a child, that's what i thought anyway.

[commoner]

I would say that under normal circumstances the odds are alway 50-50 but after five of one sex in a row there is a good chance that there is some genetic problem which prevents conception of the other sex.

[New Judge]

Yes, but leaving that aside (as bednobs has suggested we do) the odds at each and every conception are 50:50. The matter is also complicated by multiple births so it might be easier if you consider tossing a coin. Here, leaving aside the almost infinitely small possibility that the coin will come to rest on its edge, every spin is 50:50. The results of previous spins have absolutely no influence on the latest one. Of course what does change as a result of the previous spins is the odds against having consecutive heads or tails (or boys or girls). The odds against having two boys is one in four and the odds against having three is one in eight. As the number increases the odds double and this would perhaps instinctively lead one to believe that the odds on the next individual event increase in the same way. But they don’t.

[bednobs]

So, nj are you saying it's more unlikely to have 2 boys rather than a boy and a girl?

[bednobs]

sorry, you can probably see i'm having trouble grasping this.

It might help to tell the reason i'm asking - i was thinking about my family today, and all of my first cousins are either boy/boy or girl/girl combinations , including me and my sister. However, i have had girl, boy, girl. If i were to have any more children, would i be more likely to have a boy or a girl or equal?

[New Judge]

Yes.

In two births you can have:

Boy:Girl

Girl:Boy

Boy:Boy

Girl: Girl

So you can see there is one chance in the four possibilities of two boys (or indeed of two girls) but two chances of one of each.

[factor-fiction]

If the odds of having a boy was always 50% then if you were to have two children the odds of:
>two boys would be 25%;
>two girls-25%;
>and a boy and girl- 25%.

So the answer to your question would be 50%.

But as others have suggested there may be genetic factors at play which make the odds slightly different from 50/50 when it comes to the sex of a baby

[bednobs]

sorry factor - which question of mine are you answering with 50%?

[New Judge]

And the answer to your second question is "equal" (leaving aside the genetic influences, etc.).

[bednobs]

and NJ, the way you put it seems very clear, thanks

[factor-fiction]

We can't give a definite answer bednobs because of possible genetic issues- that needs bilogical expertise.

If you were asking about 50/50 chances each time such as tossing a coin then it doesn't matter what came before: the coin has no memory. So Even if you threw Heads ten times on the run it's still a 50/50 chance on the eleventh throw

[New Judge]

The odds of having one of each are 50%, factor.

[factor-fiction]

>"sorry factor - which question of mine are you answering with 50%"

At 16:50 I was answering your initial question about two children.
At 16:54 I was answering your follow-up question about a third child.
But the answers are related- the issues are the same

[factor-fiction]

Yes NJ - I did say the answer was 50% but somehow when I reformatted my answer onto separate lines I lost one of the lines - girl then boy= 25%

[jake-the-peg]

Yes and No

It depends on whether the probability is 'independent' or not.

The classic independent is tossing a 'fair' coin - then no matter how many heads you've already had the probability is always 50%.

Now - is the gender of children independent in this way?

Maybe not - maybe the man is producing many more Y sperm than X, maybe the woman's body is more receptive to one than another.

Over the entire population this comes out at 50% pretty much

But If I knew a couple that had had 6 boys I don't think I'd give you evens on a girl

[bednobs]

so just to be clear, all other things being equal, after GBG the next baby is just as likely to be a girl as a boy?

[jake-the-peg]

'all other things being equal' - yes

It's just that in real life things are not always 'equal'


----- Science Joke ----------------

A farmer asks a mathematician if he can help because his hens aren't laying

The mathematician strokes his beard and goes off to think

He comes back and says 'I have a solution....but there is a catch'

'It only works for perfectly spherical chickens!'

[bednobs]

thanks everyone.
Factor, i am still alittle confused. going back to your example of a coin toss, surely it's less likely that a coin would come up heads 100 times in a row, than to have a mixture of h/t?

[jake-the-peg]

It is less likely before you start that a coin will come up 100 times in a row

However what has happened before is 'independent' of the probability so the fact that the last 99 throws were heads does not affect the probability that the next will be heads - still 50%

[bednobs]

ok, thanks