Q: We have 3 children, they are all boys, and we now want another child. Should we give up our hope for a girl?
A: Even after 3 children of the same sex, your chances in the next pregnancy having the same one is about even. Having already 3 boys you may think it’s a foregone conclusion that the next baby is going to be another boy, but in reality, your chances are about equal between a boy and a girl. It’s not that unusual to have 3 children of the same gender in a row. This actually happens in one out of four couples who have 3 children.
You are watching: What is the probability of having 3 children that are all boys?
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Even after 3 children of the same sex, your chances in the next pregnancy having the same one is about even.
How the baby’s gender is determined
Each of the man’s sperms and each egg carry 23 chromosomes. The sperm and the egg combine at fertilization for a total of 46 chromosomes which come in 23 pairs.The 23rd chromosome is called the “sexchromosome”. In sperms, it is either an X or a Ychromosome, while in the woman’s egg it is always X.If an Xbearing sperm fertilizes the egg, the resulting 23rd pair is XX, a girl, and if a Ybearing sperm fertilizes the egg, the result is XY, a boy.It is therefore the sperm that decides the baby’s gender: Xbearing sperms result in girls, and Ybearing sperms in boys.In general, X and Ybearing sperms are about equally distributed in the ejaculate, so each time there is about an equal 5050 chance for each gender.If you already have a boy, the chance that the next baby is also a boy is 50 percent
It’s all a matter of mathematics. A couple having 4 children of the same gender in a row happens actually more often than you might think. In fact, one in eight couples (12.5%) with 4 children have 4 of the same sex.
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Here"s how it goes:
Couples with 2 children: 50% of couples have 2 girls or 2 boys, and 50% of couples have 1 girl/1 boyCouples with 3 children: 25% of couples have 3 girls or 3 boys, and 75% have 1 boy/2 girls or 1 girl/2 boysCouples with 4 children: 12.5% of couples have 4 girls or 4 boys, 37.5% will have 1/3 and 50% will have 2/2.Couples with 5 children: 6.25% have 5 the same sex and in couples with 6 children, 3.125% will have the same sex.
 All same sex  Different sexes 

2 children  50% G/B  50% B/G 

3 children  25% all girl or all boys  75% BB/G or GG/B 

4 children  12.5% all girls or all boys  37.5% 1B/3G or 1G/3B  50% BB/GG 
5 children  6.25% all boys or all girls  25% BBBB/G or GGGG/B  68.75% GGG/BB or BBB/GG 
6 children  3.125% all boys or all girls  12.5% BBBBB/G or GGGGG/B  46.875%: GGGG/BB or BBBB/GG 




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