Question

What is the probability of three daughters to a couple in three children?
(a) 1/4
(b) 1/8
(c) 1/16
(c) 3/8

Answer 1

Hint: The gender of the child is dependent on the father. Female gametes have only X chromosomes whereas the male gametes have a 50% chance of having X or Y

Complete answer:
If a couple has three children the chance of the individual child being a girl or a boy is 1/2 chance of the child being a girl and 1/2 the chance of the child being a boy. Thus if the couple were to have all-female children is 1/2 x 1/2 x 1/2 = 1/8.

The gender of the child is determined by the chromosome present. A female has XX and a male has XY chromosomes present. When gametes are formed these gametes have one of the sex chromosomes from each parent. Since women have two X chromosomes the female gamete, the egg only has X. In male gametes since males have one X and one Y there will be a 50 % chance of the sperm carrying an X or a Y. When a sperm carrying X fuses with an egg the zygote will contain XX and hence the child will be a female. If the sperm carrying Y chromosome fuses with the egg, the zygote will have XY chromosome thus the child will be a male.

Note: The sex of the child is not related to other offsprings of the same parents, gender outcomes are independent and a matter of chance. If the sex of the children of successive births remains the same, the probability of that outcome for a single-sex increase.