This situation occurs in 1-2% of monozygotic twin pregnancies.
From the en.wikipedia.org
So if one monozygotic twin, for example, develops an ailment that the other escapes, the culprit is probably environmental.
From the economist.com
The sequential cohort study included data from 749 monozygotic twin pairs and 687 dizygotic twin pairs between the age of 8 and 17 and their parents.
From the sciencedaily.com
Monozygotic twins who share a placenta can develop twin-to-twin transfusion syndrome.
From the en.wikipedia.org
Scientists scanned the brains of 15 pairs of identical, or monozygotic, twins in which one twin was schizophrenic and the other well, using magnetic resonance imaging.
From the newscientist.com
The feto-fetal transfusion syndrome affects only monozygotic twins and results in an undersupply of blood in one twin.