issues with probability a man has $4$ children, given that atleast one of whom is a girl.Find the probability that he has $3$ girls and $1$ boy.

MY TRY :

probability of girl=$1/4$ and probability of boy=$3/4$ (my doubt is here, are these two probabiity correct? because it is said that atleast one of whom is a girl , not exactly 1)

=> 4c3 * (1/4)^4 * 3/4
I would imagine that the following assumptions hold: each child is either male or female; each child has the same chance of being male as of being female; and the sex of each child is independent of the sex of the other.

If at least one of the four children is a girl, then there are 15 equally-likely possibilities: BBBG, BBGB, BBGG, BGBB, BGBG, BGGB, BGGG, GBBB, GBBG, GBGB, GBGG, GGBB, GGBG, GGGB, GGGG.  Of these, there are four equally-likely cases where he has 3 girls and 1 boy (BGGG, GBGG, GGBG, GGGB).  Thus, the probability that he has 3 girls and 1 boy given that he has at least 1 girl is 4/15.
The man has four children of which have have atleast one girl so he may have 1 girl and three boys or two girls and two boys or three girls and one boy or four girls. so the probability that he has 3 girls and one boy is 1/4.