Question: I would like to make sure I'm starting a problem correctly. I was thinking that the first two branches would be identical (1/3) and fraternal

I would like to make sure I'm starting a problem correctly. I was thinking that the first two branches would be identical (1/3) and fraternal (2/3); the branches shooting off the identical probability would be Boy&Boy (1/2) and Girl&Girl (1/2); the branches shooting off fraternal would be BB(1/3), GG(1/3) AND BG(1/3). Is my reasoning correct? The question is:

One-third of twins are identical and two-thirds of twins are fraternal. Identical twins always have the same gender, but the genders of fraternal twins are independent of one another. Suppose that a woman has an ultrasound and learns that she is pregnant with twin girls. What is the probability that they are identical twins? You may assume boys and girls are equally likely.

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