No it is not correct that in a family having three children, there may be no girl, one girl, two girls or three girls, the probability of each is ¼. .
Let boys be B and girls be G
Outcomes can be BBB , GGG , BBG , BGB , GBB, GGB, GBG , BGG
Then Probability of 3 girls = 1/8
Probability of 0 girls = 1/8
Probability of 2 girls = 3/8
Probability of 1 girl = 3/8