Given equal genetic probabilities of having an XY child or an XX child, the probability that a group of four siblings will include all XY children is 12,5%, to understand the probabilities we must understand that ......
To determine the probability, we need to know the following conditions:
The x is independent of the first, and so on.
The odds of having an Xy are equal to the odds of having an XY, ie 50%. So we have:
Xy = 1/2 = 50%
XY = 1/2 = 50%
Based on this data, we will determine the odds of the pairs given above occurring. For this situation, we use a binomial development given by
(x + y)n, where n is the number of children the couple wants to have. In this binomial, x will represent a boy and y, a girl. Note the development of the expression:
(x + y)2 → (x + y) * (x + y) → x² + xy + xy + y² → x² + 2xy + y²
x (boy) = 1/2
y (girl) = 1/2
Two boys → x² → (1/2)² → 1/4 → 25%
Two girls → y² → (1/2)² → 1/4 → 25%
A boy and a girl → 2xy → 2 * 1/2 * 1/2 → 2/4 → 1/2 → 50%
With this information, we can conclude that the chance to have a group of four siblings includes all XY is 12.5%.
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