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In , in England and Wales, for example, there were , live male births and , live female births - a difference of roughly 17, And that higher tally of males compared to females born each year is a pattern that has repeated itself for nearly years. In fact, a ratio of roughly male births for every female ones is generally seen as natural and normal. It is fairly consistent around the world, although in some countries like China and India the gap is wider because male offspring are more desirable. But why this ratio exists is not yet completely understood - although there are several theories.

The first theory is an evolutionary one which says that in order to have an equal number of males and female in adulthood, there have to be slightly more males born. That is because being a male is a dangerous thing. Males are more likely than females to die in childhood and at all stages of life - from accidents, taking risks, suicide and from health problems. So more males than females at the start of life should mean equal numbers of men and women in adulthood, so the theory goes.

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In fact, adult women always end up slightly outnumbering adult men in the UK, according to Office for National Statistics figures - and living longer. There are lots of different factors that could determine whether a male sperm carrying a Y chromosome or a female sperm carrying an X chromosome is first in the race to fertilise the woman's egg.

These include the ages of the parents, the woman's ovulation cycle, levels of stress, diet and sexual position. One popular theory is that the odds of having a girl increase by having sex several days before ovulation and then abstaining so that the female sperm, which live longer, but swim more slowly than male sperm, outlast their counterparts. Conversely, if sex happens closer to ovulation or after it, the best swimmers get to the egg first and boys are produced.

Parents may swear by these techniques, but scientists say there is little evidence they make any difference. There is also some research which suggests parental stress could lead to the birth of more girls, while living through wars and conflicts may give rise to more male conceptions.

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If planning that sexual encounter does not have an impact on a baby's sex, then could something else be happening during pregnancy? If there are equal numbers of female and male-producing sperm and roughly equal numbers of conceptions, then more female foetuses must perish to give males the upper hand. Some research suggests females are more likely to be lost in the womb during early pregnancy, but other studies have shown males foetuses are more fragile later in pregnancy and lead to more stillbirths.


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But if B is deduced from C , then it is not reasonable to conclude A. This point was made eloquently by Pearl p He used it to show that logic based on "certainty factors" is not an adequate replacement for probability theory. But sometimes we drop relevant information without realizing it.

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Consider this example:. My neighbor has two children. Suppose I ask him whether he has any boys, and he says yes. What is the probability that one child is a girl?

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Bayes' rule will give the same result. Suppose instead that I happen to see one of his children run by, and it is a boy. What is the probability that the other child is a girl? In fact that is what Bayes' rule says in this case.

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If you don't believe this, draw a tree describing the possible states of the world and the possible observations, along with the probabilities of each leaf. Condition on the event observed by setting all contradictory leaf probabilities to zero and renormalizing the nonzero leaves. The two cases have two different trees and thus two different answers. This seems like a paradox because it seems that in both cases we could condition on the fact that "at least one child is a boy.


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  • In the first case, the event was "He said yes to my question. Probabilities reflect the number of possible ways an event can happen, like the number of roads to a town.

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    Logical implications are further down the road and may be reached in more ways, through different towns.