Probability problem

Originally posted by Omnislash
With a completely systematic 50/50 ratio I agree that it would do nothing. Like I said, my concern is the genetic variants that could produce something other than a 50/50 ratio. The data within the question suggests that such a genetic disposition already exists which favors female births (i.e. a genetic variant which is not conducive to the acceptance of the male gender producing XY chromosome).

Actually the data don't suggest this at all. The original problem simply stated "the government feels the propotion of girl babies" is too high. Occam's razor would argue against drawing the conclusion that the people in this land suffer from some genetic abnormality. A far better conclusion to draw is that the government simply wants more boys than girls....

Originally posted by The Plumber
Actually the data don't suggest this at all. The original problem simply stated "the government feels the propotion of girl babies" is too high. Occam's razor would argue against drawing the conclusion that the people in this land suffer from some genetic abnormality. A far better conclusion to draw is that the government simply wants more boys than girls....

My friend, I truly do not wish to quarrel with you when I simply mean to speculate overtly upon a query whose answer does not require any such speculation to be answer as it was intended. If you so choose to read the data differently than me than you are quite welcome to do so and I applaud your difference in perspective.

However, I would like to share my thought on your reference of Occam's razor. Your hypothesis would infer that the government seeks to unbalance the populace gender wise. My hypothesis would infer that the government seeks to balance a populace which is imbalanced gender wise. If you so wish to claim that your proposed assumptive logic holds the simplest answer, that is of your own accord to do so. I disagree, but likewise admit that my own assumptive logic has nothing more substantial behind it than yours. Simply a difference of perspective.

....and the ratio is still 1:1. 😉

Best Regards,
Omnislash

P.S. Just as an after thought. I have always wondered to myself about Occam. If all things are equal and the simplest answer is usually correct, would that infer inaction? Just a philosophical/scientific/asinine thought I've wanted to share for a while. 😀

Originally posted by Omnislash
My friend, I truly do not wish to quarrel with you.... Simply a difference of perspective.

Agreed....

P.S. Just as an after thought. I have always wondered to myself about Occam. If all things are equal and the simplest answer is usually correct, would that infer inaction? Just a philosophical/scientific/asinine thought I've wanted to share for a while. 😀

Depends.... Is inaction simpler than action?

Originally posted by Omnislash
The answer is impossible to determine due to undefined variables.

You're right. I'll give you one more assumption: a woman's previous children don't affect her likelihood of giving birth to boys as opposed to girls. What can you now say?

Any country who is so evolved to recommend this fantastic idea has most likely been tainted by a lust for total control (kbg/cia equivalent) so the girls r dead neway. gg

Originally posted by Omnislash
With a completely systematic 50/50 ratio I agree that it would do nothing. Like I said, my concern is the genetic variants that could produce something other than a 50/50 ratio. The data within the question suggests that such a genetic di ...[text shortened]... you are correct.

Best Regards,
Omnislash

I tend to agree partially with your view. The contention that in every birth the probability of a male or a female child being born is equal , is obviously not the case in the Land of Misogynia , as , there is a skewed population of baby girls to begin with.

Apart from this wrong premise, the further wrong assumption involved in the calculation of TheMasters37 and Cheskmate is that , each couple would have an infinite no. of successful conceptions with 100% certainty , but for the restriction imposed by the new policy of the Govt of Misogynia. If that were the case , in the absence of this policy, each couple would have a
family size ( average no. of children per couple) of infinity , in principle.

Obviously this was not the case , even before the new policy , introduced apparently for correcting the skewness , was brought into force. Therfore for a realistic calculation we will have to make allowance for the progressive decrease in the probability of the success of each conception starting from the first conception onwards. This will be based on the average family size prior to the new policy. Secondly , we will have to assume that upon successful conception, the probability of birth of male child is 0.5 - x, and that of a female child is 0.5 + x, where x is a small fraction deducible from the skewness prior to the new policy.

For example if the pre- policy average family size (average no. of children per couple) is m, then the probability of success of each successive conception will go down by a factor of (m -1)/m, as compared to the probability of success of the preceding conception..

Taking both these into account , we would have to, then work out the average family size n , (after the policy is in place), according to the above model, following the method of TheMasters37. Obviously n will depend on m and x as mentioned in the preceding paragraph. Thus the post-new policy female to male child ratio will eventually stabilise at 1/ (n - 1).

Originally posted by ranjan sinha
I tend to agree partially with your view. The contention that in every birth the probability of a male or a female child being born is equal , which obviously is not the case in the Land of Misogy ...[text shortened]... ost-new policy female to male child ratio will be 1/ (n - 1).

None of this actually makes a difference as to whether the government's policy increases or reduces the proportion of girls. If the sex of a child is independent of its mother, their policy will have no effect on the proportions.

Originally posted by ranjan sinha
I tend to agree partially with your view. The contention that in every birth the probability of a male or a female child being born is equal , is obviously not the case in the Land of Misogynia , as , there is a skewed population of baby girls to begin with.

Apart from this wrong premise, t ...[text shortened]... post-new policy female to male child ratio will eventually stabilise at 1/ (n - 1).

Well, the fact that there are more girls then boys doesn't mean anything about the chances of getting a girl-child.

Just like tossing a coin alot of times. Statistically, there HAS to be a long chain of heads, and also a long chain of tails in it.

That there are more girls then boys is statistically alright. The ratio of head vs tails is 1:1 only for an infinite experiment. In an finite experiment the ratio may vary.

And maybe the boys were in a large group sent out to war with the neighbouring country and all killed in action.

If we bring this problem into the "real world", we get a very surprising result - this policy will affect the ratio of boys to girls, but in the opposite manner to which the government intended!

The above statement is true given the following assumptions:

1. The chance of giving birth to either a boy or a girl is 50%.
2. The number of families is infinite (so that the statistical limit matches the observed ratio).
3. Mothers will eventually refuse to have any more children after some maximum limit is reached. (Ask any mother - this assumption is the most reasonable one of the three. Why do you think they invented the "headache"?)

As discussed in earlier posts, the expected number of boys in a family with no maximum limit asymptotically approaches 1, and the number of girls is always 1, so the ratio approaches 1:1. However, for any maximum family size less than infinity, there is a slight but definite surplus of girls. For example, if the maximum limit is 5 children, the ratio of boys to girls is approximately 0.89:1. For a limit of 8, the ratio is 0.98:1. For limits of 11 or higher, the ratio rounds off to 1.00:1, but imagine the dental costs alone for a family that size...scary.

So essentially the government is shooting itself in the face with a policy like this. Lousy misogynists.

Originally posted by PBE6
If we bring this problem into the "real world", we get a very surprising result - this policy will affect the ratio of boys to girls, but in the opposite manner to which the government intended!

The above statement is true given the following assumptions:

1. The chance of giving birth to either a boy or a girl is 50%.
2. The number of families is inf ...[text shortened]... ially the government is shooting itself in the face with a policy like this. Lousy misogynists.

Actually...no. Like Dr. Scribbles said, banning people for flipping heads won't change the probability of the next toss of the person who flipped tails.

Example:
0.4 = P(boy)
0.6 = P(girl)

- Families who want 1 kid.
E(boys) = 0.4
E(girls) = 0.6
E(total of kids) = 1
Proportion of boys = 0.4
Proportion of girls = 0.6

- Families who want 2 kids
E(boys) = 2*0.4^2 + 0.4*0.6 = 0.56
E(girls) = 0.6+0.4*0.6 = 0.84
E(total) = 1.4
Proportion of boys = 0.56 / 1.4 = 0.4
Proportion of girls = 0.84 / 1.4 = 0.6

- Families who want 3 kids
E(boys) = 3*0.4^3+2*0.4^2*0.6+0.4*0.6 = 0.624
E(girls) = 0.6 + 0.4*0.6+0.4^2+0.6 = 0.936
E(total) = 1.56
Proportion of boys = 0.624 / 1.56 = 0.4
Proportion of girls = 0.936 / 1.56 = 0.6

And so on.

Families who want n kids.
E(boys) = n*0.4^n + 0.6*(n-1)*0.4^(n-1) + 0.6*(n-2)*0.4^(n-2) ... 0*0.6
#Note: E(boys) = 0.4* [n*0.4^(n-1)+0.6*(n-1)*0.4^(n-2)+...

E(girls) = 0.4^(n-1)*0.6+0.4^(n-2)*0.6+...+ 0.4^(n-n)*0.6
E(total) = n*0.4^(n-1)+0.6*((n-1)*0.4^(n-2)+(n-2)*0.4^(n-3)+...)

Proportion of boys = E(boys)/E(total)=0.4*E(total)/E(total) - see #Note
= 0.4
Proportion of girls = 1 - Proportion of Boys = 0.6

Hope I haven't made any typo in the equations there...

For any probability P(boy) = x, substitute 0.4 for x and 0.6 for (1-x)

Originally posted by PBE6
and the number of girls is always 1

Why can't it be zero?

Originally posted by Acolyte
Why can't it be zero?

Too true. I assumed that each family would be finalized with the birth of a girl, but that is not necessarily the case.

I just proved mathematically why the proportion stays constant.

The logical proof is simple. Whenever a woman has a child, it's sex doesn't depend on ANY previous births (whether hers or from other mothers).

Originally posted by Palynka
I just proved mathematically why the proportion stays constant.

The logical proof is simple. Whenever a woman has a child, it's sex doesn't depend on ANY previous births (whether hers or from other mothers).

What, do you want a prize? Here, have a gold star. Have 5 of them. Are you special yet? Have 10. Now you have something to tell mom about! Way to go, Palynka!

Originally posted by PBE6
What, do you want a prize? Here, have a gold star. Have 5 of them. Are you special yet? Have 10. Now you have something to tell mom about! Way to go, Palynka!

No thanks, but hey, have a Valium. I think you need it...