2. Twins make up a small fraction of the human population. Identical monozygotic

Question

2. Twins make up a small fraction of the human population. Identical monozygotic twins make up 8% of all twins Identical twins always have the same sex. The other 92% of twins are called dizygotic or fraternal. In a family having two children who are not identical twins, the sex of each child is independent and each sex has probability 1/2. a) In the cases in which the two children are not twins, what is the probability that both children are girls? b) In the cases in which the two children are twins, what is the probability that both children are girls? c) If the twins are both girls, what is the probability that they are identical twins?

Explanation / Answer

ANSWER :-

(a)

If two children are not twins probability that the both children are girls is P = (1/2) * (1/2) = 0.25

(b)

If two children are twins, It means that they may be identical or dizygotic.

Now, the probability that the both children are girls is P = 0.08 + (0.92 * 1/2) = 0.08 + 0.46 = 0.54

(c)

If both twins are girls then the probability that they are identical is P = 0.08 / (0.08 +0.92 ) = 0.08

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