How do parents give their offspring a chromosome?
Are the laws of physics deterministic? I think no one knows, currently.

In any event, yes, the segregation of homologous chromosomes during meiosis I is random: there is an equal probability for each chromosome of a homologous pair to segregate into a given gamete, and this is independent of other homologous pairs. This idea dates back to Mendel, who observed that the heritable “factors” (what we now know as genes) responsible for macroscopic phenotypes are inherited independently of one another (this is his Law of Independent Assortment). This isn’t actually true when considering linked genes, but is certainly true of chromosomes, as was described by Sutton in 1903:


  ...many points were discovered which strongly indicate that the position of the bivalent chromosomes in the equatorial plate of the reducing division is purely a matter of chance - that is, that any chromosome pair may lie with maternal or paternal chromatid indifferently toward either pole irrespective of the positions of other pairs...