It is known that about 30% of human twins are identical and the rest are fratern

Question

It is known that about 30% of human twins are identical and the rest are fraternal.
Identical twins are necessarily the same sex | half are females and the other half are males.
Furthermore, one-quarter of fraternal twins are both male, one-quarter are both female,
and one-half are mixed (one male and one female).
(a). What is the probability that the randomly selected twins are twin boys?
(b). Given that a couple has just become the parents of twin girls, what is the probability
the twins are identical?

Explanation / Answer

Let

I = identical
F = fraternal
BB = both boys
BG = mixed
GG = both girls

a)

P(BB) = P(I) P(BB|I) + P(F) P(BB|F)

= 0.30*0.5 + (1-0.30)*0.25

= 0.325 [ANSWER]

****************

b)

P(I|GG) = P(I) P(GG|I) / P(GG)

As

P(GG) = P(I) P(GG|I) + P(F) P(GG|F) = 0.30*0.5 + (1-0.30)*0.25 = 0.325

Then

P(I|GG) = P(I) P(GG|I) / P(GG)

= 0.30*0.50/0.325

= 0.461538462 [ANSWER]

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