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Upon fertilization, the resulting embryo receives 23 pairs of chromosomes. Only one of these 23 pairs will determine the sex of the child at conception. This is pair 23 (represented by chromosomes 45 and 46).
In the following two images, look closely at the last chromosomes. For women, there are two X chromosomes and no Y. In men, there is one X and one Y chromosome.

Chromosomes of a Woman

Chromosomes of a Man
The ovum that will be fertilized carries X chromosomes, while the spermatozoa carry X or Y chromosomes in equal proportions. It is therefore the father’s winning spermatozoon (the one that will fertilize the ovum) which will determine the sex of the unborn child.
If an X-chromosome sperm fertilizes an ovum (still carrying X chromosomes), it will be a girl. Pair 23 will be represented by XX chromosomes.
If a Y-chromosome sperm fertilizes the ovum (still carrying X chromosomes), it will be a boy. Pair 23 will be represented by XY chromosomes.