Can anyone help me in understanding how backcrossing helps hybrid to achieve pureline?

I have been looking into the references i possess but couldn't seem to find anything


Back crossing is the process by which a hybrid organism is crossed back (backcrossed) into a pure organism. Let's see an example

Organism 1 is heterozygous for a single gene (e.g. a hybrid), which has alleles that we can call $A$ and $a$. We can write that organism's genotype.

Organism 1 Genotype: $Aa$ (100% chance)

Right now, there is a 0% chance that organism 1's genotype is $AA$.

Goal: increase probability that organism 1's genotype is $AA$

One way to achieve this goal is to cross Organism 1 with another organism, let's call it Organsm 2, that is has a homozygous (e.g pure) genotype of $AA$.

So if Organism 1 is crossed with Organism 2 and produces a new Organism 3 what is its genotype? Well, we're not sure.

Organism 3 Genotype: $AA$ (50% chance)

Organism 3 Genotype: $Aa$ (50% chance)

Now we do the same thing again, to get Organism 4

Organism 4 Genotype: $AA$ (75% chance)

Organism 4 Genotype: $Aa$ (25% chance).

This effect keeps compounding, until there is a very high chance that the final organism has a pure (e.g. $AA$) genotype.


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