If a parent has genotype Aa, he transmits either A or a to an offspring (each with a 1/ 2 chance). The gene he transmits to one offspring is independent of the one he transmits to another. Consider a parent with three children and the following events: A ={children 1 and 2 have the same gene}, B ={children 1 and 3 have the same gene}, C ={children 2 and 3 have the same gene}. Show that these events are pairwise independent but not mutually independent.
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