# What are the odds of hatching 11 roosters and 1 hen?

I bought one dozen fertililized eggs, incubated them and hatched 11 roosters and 1 hen! This was just the opposite of what I'd hoped. What were the odds of this happening?

-
Congratulations, but it depends on many factors. I don't think that the probability of male or female hatchlings is a half. It could well depend on temperature besides many other factors. –  BlackAdder Feb 21 at 1:07

Depends on how hot the incubator was:

There was no difference in sex ratio between chickens hatched from eggs stored at 60 and 80°F, neither departing significantly from 50 per cent. pullets. However, storage at 40°F produced significantly more pullets than cockerels, 54.6 per cent. of the chickens being pullets

Taken from this study: http://www.publish.csiro.au/paper/AR9600664.htm

So for 50% it's $${12 \choose {1}}*2*(1/2)^{12} = 3/512 \approx 0.006%$$

For 54% pullets or female chickens,

$${12 \choose {1}}*2*(.546)^{11} *(.454) \approx 0.01%$$

-

If you think the innate odds are $50\%$ for each, the chance of getting a split of $11-1$ (either way) is $2{12 \choose 1}(\frac 12)^{12}=\frac {24}{4096}\approx 0.006$ You were either unlucky or the odds are not $50-50$

-

Assuming that the probability of getting a hen and a rooster is equal, it's follows a binomial distribution with $P=0.5$ of success:

$${12 \choose 1}\cdot(0.5)^{12-1}\cdot(0.5)^1=12\cdot(0.5)^{12}\approx 0.3\%$$

This is the chance of getting 11 roosters and a hen.

-