I'm not sure about where you get the half.

Consider the 3 pairs of chromosomes... A, B, & C.

Father (paternal) has the genes, 3 pairs (6 chromosomes total) (A0pA1pB0pB1pC0pC1p)

A0p, A1p

B0p, B1p

C0p, C1p

Mother (maternal) has the genes, 3 pairs (6 chromosomes total) (A0mA1mB0mB1mC0mC1m)

A0m, A1m

B0m, B1m

C0m, C1m

Father can create the possible haploid combinations (2

^{3} = 8 total)

A0pB0pC0p

A0pB0pC1p

A0pB1pC0p

A0pB1pC1p

A1pB0pC0p

A1pB0pC1p

A1pB1pC0p

A1pB1pC1p

Mother can produce the haploid combinations: (2

^{3} = 8 total)

A0mB0mC0m

A0mB0mC1m

A0mB1mC0m

A0mB1mC1m

A1mB0mC0m

A1mB0mC1m

A1mB1mC0m

A1mB1mC1m

So, now you get 8 paternal haploid combinations, and 8 maternal haploid combinations... 2

^{3} * 2

^{3} = 2

^{6} = 8*8 = 64 diploid combinations.

Do I need to list out the entire list? (written in 2 separate columns to save space). 64 total.

A0mB0mC0mA0pB0pC0p A1mB0mC0mA0pB0pC0p

A0mB0mC0mA0pB0pC1p A1mB0mC0mA0pB0pC1p

A0mB0mC0mA0pB1pC0p A1mB0mC0mA0pB1pC0p

A0mB0mC0mA0pB1pC1p A1mB0mC0mA0pB1pC1p

A0mB0mC0mA1pB0pC0p A1mB0mC0mA1pB0pC0p

A0mB0mC0mA1pB0pC1p A1mB0mC0mA1pB0pC1p

A0mB0mC0mA1pB1pC0p A1mB0mC0mA1pB1pC0p

A0mB0mC0mA1pB1pC1p A1mB0mC0mA1pB1pC1p

A0mB0mC1mA0pB0pC0p A1mB0mC1mA0pB0pC0p

A0mB0mC1mA0pB0pC1p A1mB0mC1mA0pB0pC1p

A0mB0mC1mA0pB1pC0p A1mB0mC1mA0pB1pC0p

A0mB0mC1mA0pB1pC1p A1mB0mC1mA0pB1pC1p

A0mB0mC1mA1pB0pC0p A1mB0mC1mA1pB0pC0p

A0mB0mC1mA1pB0pC1p A1mB0mC1mA1pB0pC1p

A0mB0mC1mA1pB1pC0p A1mB0mC1mA1pB1pC0p

A0mB0mC1mA1pB1pC1p A1mB0mC1mA1pB1pC1p

A0mB1mC0mA0pB0pC0p A1mB1mC0mA0pB0pC0p

A0mB1mC0mA0pB0pC1p A1mB1mC0mA0pB0pC1p

A0mB1mC0mA0pB1pC0p A1mB1mC0mA0pB1pC0p

A0mB1mC0mA0pB1pC1p A1mB1mC0mA0pB1pC1p

A0mB1mC0mA1pB0pC0p A1mB1mC0mA1pB0pC0p

A0mB1mC0mA1pB0pC1p A1mB1mC0mA1pB0pC1p

A0mB1mC0mA1pB1pC0p A1mB1mC0mA1pB1pC0p

A0mB1mC0mA1pB1pC1p A1mB1mC0mA1pB1pC1p

A0mB1mC1mA0pB0pC0p A1mB1mC1mA0pB0pC0p

A0mB1mC1mA0pB0pC1p A1mB1mC1mA0pB0pC1p

A0mB1mC1mA0pB1pC0p A1mB1mC1mA0pB1pC0p

A0mB1mC1mA0pB1pC1p A1mB1mC1mA0pB1pC1p

A0mB1mC1mA1pB0pC0p A1mB1mC1mA1pB0pC0p

A0mB1mC1mA1pB0pC1p A1mB1mC1mA1pB0pC1p

A0mB1mC1mA1pB1pC0p A1mB1mC1mA1pB1pC0p

A0mB1mC1mA1pB1pC1p A1mB1mC1mA1pB1pC1p

So, extrapolating to 23 pairs of chromosomes, you get 2

^{23}*2

^{23} = 2

^{46} = 1 in 70,368,744,177,664 chance.

If the average babies per couple was 1, i dont think you could have cousins, therefore 0 probability. But this is not the case, as the population (as you said) will eventually decline and die out.

Good point about no cousins, at least back to the point where one started the 1 child policy. So you're just left with Oedipus.

I have always wondered why China's population is still increasing with a 1 child policy.

By anti-twin i presume you mean another sibling from the same couple with the opposite chromosome combination of you.

This would be the same probability as creating an exact twin - the probability of getting ANY gene combination is 1 in 1.76X10 ^{13}.

True... except there will be 1 sperm, and 1 egg that has the exact opposite genes.

The likelihood of the second egg getting fertilized either at the same time (fraternal twins), or during successive pregnancies is non-zero. So, if fertilization is "random", with fraternal twins, it would depend on the number of sperm per ejaculate, and would be around 1 in 280 Million (assuming both sperm are viable in the same ejaculate).

For successive pregnancies, it depends on the chance of that second egg getting fertilized times the probability of the "anti-twin" sperm, which as mentioned, with no crossovers, it is actually a smaller number 1 in 2

^{23} for the men (1 in 8,388,608), but in reality is a more rare case due to the crossovers.

Without getting that second egg... the obviously the number is the same as the one calculated above... 1 in 70 trillion.

(did I say quadrillion earlier... I guess I meant trillion).

I wonder if the female's egg would account for why many fraternal twins have a high degree of differences.

-------------------------------------