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Assuming probability of having a boy is P(B) = 1/2, and of having a girl is P(G) = 1/2,the probability of having 3 boys for 4 kids (with out regard to the girl to be the first,second, third or fourth kid) is;P(3B1G) = 4C3 [P(B)]4 = 4 (1/2)4 = 0.250 = 25%The factor 4 comes because there are 4 possibilities for the order in which the girl cancome out.
If we consider there is a 50% chance for having a boy and 50% for having a girl*, there is : - 12,5% chance of having no boys; - 37,5% chance of having 1 boy; - 37,5% chance of having 2 boys; - 12,5% chance of having 3 boys. Therefore, there is 50% chance of having at least two boys. *The odds are more like 51% for having a boy and 49% for having a girl, but it doesn't really matters.
There is no simple answer to the question because the children's genders are not independent events. They depend on the parents' ages and their genes.However, if you assume that they are independent events then, given that the probability of a boy is approx 0.52, the probability of three boys and a girl is 0.2669.
There is only one girl out of 12 students so the probability that the girl is selected is 1/12.