Common Assumptions
The two possible answers share a number of assumptions. First, it is assumed that the space of all possible events can be easily enumerated, providing an extensional definition of outcomes: {BB, BG, GB, GG}. This notation indicates that there are four possible combinations of children, labeling boys B and girls G, and using the first letter to represent the older child. Second, it is assumed that these outcomes are equally probable. This implies the following model, a Bernoulli process with :
- Each child is either male or female.
- Each child has the same chance of being male as of being female.
- The sex of each child is independent of the sex of the other.
In reality, this is a rather inaccurate model, since it ignores (amongst other factors) the fact that the ratio of boys to girls is not exactly 50:50, the possibility of identical twins (who are always the same sex), and the possibility of an intersex child. However, this problem is about probability and not biology. The mathematical outcome would be the same if it were phrased in terms of a coin toss.
Read more about this topic: Boy Or Girl Paradox
Famous quotes containing the words common and/or assumptions:
“Panurge was of medium stature, neither too large, nor too small ... and subject by nature to a malady known at the time as “Money-deficiency,”Ma singular hardship; nevertheless, he had sixty-three ways of finding some for his needs, the most honorable and common of which was by a form of larceny practiced furtively.”
—François Rabelais (1494–1553)
“Assumptions of male superiority are as widespread and deep rooted and every bit as crippling to the woman as the assumptions of white supremacy are to the Negro.... this is no more a man’s world than it is a white world.”
—Student Non-Violent Coordinating Committee, African American civil rights organization. SNCC Position Paper (Women in the Movement)