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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.
Since the probability of having a son is about 1/2, the probability of the first 4 children being boys is about (1/2)4.
There is only one girl out of 12 students so the probability that the girl is selected is 1/12.