This is also confirmed in Bhagavad-gītā (aprāpya māṁ nivartante mṛtyu-saṁsāra-vartmani (BG 9.3)).
There is no such thing as chance. When a tree is burning in a forest fire and although the nearest tree is spared a distant tree catches fire, this may appear to be chance. Similarly, one may seem to get different types of bodies by chance, but actually one receives these bodies because of the mind. The mind flickers between accepting and rejecting, and according to the acceptance and rejection of the mind, we receive different types of bodies, although we superficially seem to obtain these bodies by chance. Even if we accept the theory of chance, the immediate cause for the change of body is the agitation of the mind.
Notes on aṁśa. This chapter describes that Kṛṣṇa appeared aṁśena, with His parts and parcels or His partial manifestation.