Hello, I had a question that tended to cause many disagreements pertaining to genetics. Here it is:

 

What is the probability of two parents producing 3 offspring all of the same gender? They can be boy or girl.

 

I have heard 1/8 and 1/4 does anyone have a definitive answer?

[math]\left(\frac{1}{2}\right)^{3} = \frac{1}{8}[/math]

1/8 if it was completely random but it depends entirely on the sperm. it could be that the father has more X or Y type sperm for a variety of reasons. this would skew the probability somewhat.

The probability of getting all boys is 1/8 and the probability of getting all girls is 1/8 however it can be either three boys or 3 girls so...

 

It's 1/4. There is a 50% chance of getting a boy. So the chance of getting 3 boys is:

1/2 * 1/2 *1/2 = 1/8

And there is the same probability of getting 3 girls. So the total chance of getting all children of the same sex is:

1/8 +1/8 = 2/8 = 1/4

 

More proof:

The odds are 25%, since there are equal odds of having 3 boys and 3 girls.

 

50% x 50% x 50% x2= 1/4

Of course, the probability to have 3 boys is ~1/8, + ~1/8 for girls = 1/4. There's only 8 (2³) possible combinations, so it's easy to check all of them;

 

bbb

bgb

bbg

bgg

gbb

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