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Since there are four children in this family then, number of girls can either be 0(no girl), 1(there is only one girl), 2(there are two girls only), 3(there are three girls) or 4(all the children are girls). Therefore the random variable X can take on values, 0,1,2,3,4.
Hence, possible values for X: 0, 1, 2, 3, and 4.