How does the passing of genes from two parents to the offspring work?

The green genes and gray genes included.

Small example of what I'm trying to say:

The mother has a green gene agile paws and a gray gene of normal paws, the father has a green gene of massive hooves and a gray gene of small hooves. What will their baby have?

Thanks to anyone who understood this,

Autobot~Decepticon

I guess it's depending on the gene's power,for example Normal paws has power 70 and Agile paws has power 90,the baby will have a higher chance to inherit the genes with a higher power.

No.

It's random. The mother will pass on one of her two and the father will give one of his two. Which one is entirely up to chance. 50% chance that the baby will get Agile Paws and 50% that it will get Normal Paws from the mother. 

The green and grey is only for the game to evaluate AFTER the baby got the genes, which of those new genes it got from both parents will be the more powerful - so the one that "does" something. In your case, if the baby got Agile Paws this has the most power out of all the genes here, so the baby would have green Agile Paws and with that the bonus of 25% more Agility. To see Power of genes you can hover over the gene name or go to the Genes list in the help menu.

If you need any further clarification, do not hesitate to ask :) 

It is not random, according to FAQ. There it says that, dominance is determined by that very power of the gene, meaning genes with higher power have a higher chance to become dominant.

As for the "small example" in the first post:

Agile paws - gene power 90

Normal paws - gene power 70

Small hooves - gene power 60

Massive hooves - gene power 50

Ehm... The POWER is not random, but which gene will be passed down from the mother and father is still entirely random!

Once it has been decided which genes the baby will get, THEN the power comes into play and will decide which gene is dominant and which recessive. "Dominance" only means how strong it is in comparison to the second gene the baby got. Since Agile Paws is the strongest, it will always be expressed, no matter what the other gene would be (Massive Hooves or Small Hooves from the father). And even if the baby gets Normal Paws from the mother, this is still stronger than the father's Massive or SMall Hooves, so it is not possible for the baby to get those "expressed" / dominant.

From the FAQ: Your pet's offsprings will inherit the genes from the left and right columns with equal probability, the division to columns is visual only.

To make it clear with your example: Your baby might get:

Agile Paws / Massive Hooves  or
Agile Paws / Small Hooves or
Normal Paws / Massive Hooves or
Normal Paws  / Small Hooves

Which of these outcomes it will be is still completely random though. All these genes have the same chance to get passed on.

According to the first post, mother has dominant agile paws in one column, and recessive normal paws in the other column. At the same time, father has dominant massive hooves in one column and recessive small hooves in the other column.

The "randomness" (50% chance) is in where will the gene for paws come from. If from the mother, then it will more likely be agile paws, due to its gene power. If from the father, then it will more likely be small hooves, due to its gene power.

What? 

No, because the baby WILL get one gene from the mother and one from the father, no matter what... Also from the FAQ: The genes in the left column are inherited from mother, in the right - from father. 

When you look at any of your pets, the left hand side of its genes are ALL inherited from the mother, ALL right side genes are from the father. There is no 50% anything in that. If you went by what you're suggesting (if I understand you correctly), it would be in theory possible for the pet in this example to get both Massive and Small Hooves from the father and sorry, but that is absolutely, completely impossible.

So, it will get one gene from the mother 100% and one gene from the father 100%. Thus, the 50% chance only applies to which gene from the mother and which gene from the father will be passed on. 

--

I know I saw Angel post something about this once, but since I have to go to bed, I could only do a quick search, which yielded this thread here: http://beastkeeper.com/thread/1603 
Might still be interesting.

The thread found (1603), as well as FAQ, tell us the same thing; "gene dominance is determined by gene power."

How is breeding the negative genes out of the gene pool possible? Due to negative genes having lower gene power, and therefore higher chance in becoming recessive, rather than dominant.

One gene will come from the mother.

(In this case it will more likely be agile paws, due to its gene power.)

One gene will come from the father.

(In this case it will more likely be small hooves, due to its gene power.)

Out of these two, agile paws will likely be dominant, due to its gene power.

Timain is correct. The phrase "gene dominance is determined by gene power" means that of the two genes a pet inherits, the expressed gene will always be the one with the higher gene power. Dominance =/= inheritance. First to be determined is gene inheritance, which is random, and then dominance, which depends on gene power and only chooses between the two genes the offspring has already inherited. 

Recall Mendel's Laws of Inheritance, if it helps. To paraphrase:

1. Each parent only passes one allele per gene to the offspring.

2. The inheritance of each allele is unrelated to any other gene, i.e., is random.

3. A dominant allele in a gene expresses over a recessive allele.

Okay, thanks everyone. I'm sorry if that question stirred some negative feelings......I appreciate the answers!