In over 99.9% of cases identical twins will be the same sex - they are what it says on the tin, identical. 1 egg, 1 sperm, 2 babies.
However, there is a very rare anomolie that occurs where you can get twins that have come from the same egg and sperm but are opposite sexes. There have been three recorded cases of this.
http://www.bellaonline.com/articles/art1291.asp
Quote;
'Although extremely rare, there are now documented cases of boy/girl identical twins.
... the phenomena could realistically take place ... with an egg being fertilized by one sperm, then dividing itself into two separate eggs, which is also the exact way identical same-gendered twins begin life.
However, in the case of boy/girl identical twins, those fertilized eggs initially both contain male DNA only.
We all learned in high school biology that male DNA have an X-chromosome and a Y-chromosome and it’s the Y-chromosome which makes him male and female DNA have two X-chromosomes. Well, in the case of mixed-gendered identical twins, which always begin male, the Y-chromosome disappears, and science has offered no explanation for it.
As a result of losing the Y-chromosome, the male twin becomes female with an XO DNA chromosome pairing. '
It is explained even better here:
http://www.bio-medicine.org/biology-definition/Twin/#Mixed_sex_identical_twins
Mixed sex identical twins
In extremely rare cases, identical twins have been born with opposite sexes (one male, one female). In these cases, identical twin boys are conceived, but, during the twinning process, one twin loses a Y chromosome (boys have chromosome type XY while girls have XX). Without a Y chromosome to trigger the production of male sex hormones , this fetus develops as a girl by default, but a girl with only one X chromosome (chromosome type XO). The co-twin is unaffected, and develops as a boy as normal.
As a result of her genetic abnormality, the girl will suffer from Turner syndrome, which is distinguishable by short stature, folds of skin at the neck, abnormal development of secondary sexual characteristics, and an intellectual deficit known as space-form blindness . Turner syndrome can occur in any birth (including singletons, fraternal female twins, or identical female twins), so an individual with Turner syndrome is not automatically a twin. Turner syndrome occurs in about 1 in 10,000 of all births, but cases of mixed sex identical twins are much rarer—only three cases have been documented.
All this aside, your friend is WRONG as 2 egg in one sperm would cause a miscarriage or Molar Pregnancy, not opposite sex twins. Identical twins have to have the same egg and sperm.
(There is one recorded exception where twins occured due to two sperm in one egg but they were only semi-identical)
http://news.softpedia.com/news/Shocking-Semi-Identical-Twins-One-is-Hermaphrodite-50415.shtml
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