A simple distribution problem

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Antibodies are large proteins with 2 equal halves. After analysis in which we break apart the two halves, we find we have a modification at one location on 20% of the total protein. For the intact antibody, this modification can occur on both halves (2 per antibody) or only on one half (1 per antibody). If 0 = a half with no modification and + = a half with the modification, then what is the predicted distribution (% of total whole antibody) of the three modification states, 00, 0+, and ++? Our N is in moles (10 to the 23rd power) and therefore, assuming the 1st modification doesn't affect the 2nd occuring on the same antibody, I should be able to derive an almost exact result.

I have been using prob(+) = 0.2 and prob(0) = (1 - prob(+)) = 0.8, so
prob(00) = (0.8)*(0.8) = 0.64
prob(0,+) = (0.8)*(0.2) = 0.16 (*2 degeneracy = 0.32)
and prob(+,+) = (0.2)*(0.2) = 0.04

Am I correct? If so, what is the proper statistical description (i.e. fundamental distribution formula I can refer to)? If not, correct me please. I am not able to statistically explain (in a formula) the degeneracy (instead resorted to Mendel and basic genetics). I am hoping I am pretty close but would like to fill the logic gaps so I can explain properly to others.

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  • #2
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You are correct. The x 2 factor results from counting +- and -+ as the same.