Question about farmville mystery eggs?

I'm wondering exactly how these work. *****Say I decide to spend the money on a golden chicken. Every 'mystery egg' that that chicken hatches will go to a friend, and I will not be able to use it to get a hot tub or another golden chicken so I won't have to spend money on another one-is this... show more I'm wondering exactly how these work. *****Say I decide to spend the money on a golden chicken. Every 'mystery egg' that that chicken hatches will go to a friend, and I will not be able to use it to get a hot tub or another golden chicken so I won't have to spend money on another one-is this right?******* Also I have had a chicken coop for about a week been emptying it every day (I have brown chickens and white so far) and so far- no mystery eggs. Am I doing something wrong?

Any help would be greatly appreciated Thank you!
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