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
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