Why does genetic varation increase the chance that some organisms in a population will survive

Genetic variance increases the chance of survival because through an enlarged gene pool, the chances of successful mutations is higher, as well as the favoring of successful traits.
An example of this is in birds, some species with large gene pools in a single geographic location will favor males with longer tail feathers, therefore that trait will become more common and increase the chance of survival through improved genetics within offspring. 

Genetic Variation helps increase the chances a group of organisms has to survive by providing different genetics so that a species can survive. For example, if a disease breaks out into a particular species, if a few of them have immunity to that disease, then those few will survive and be able to continue on the species.

4, two dominant and two recessive