My Raspberries are randomly turning white - about 1/4 to 1/3 of them.

Symptom(s): 

The berries turn gray or white.

Cause(s):

Suspect gray mold.

Control(s):

Can be treated with a bleach solution.

As with most new small plants from the nursery, you might want to consider removing all blooms the first year and half of the blooms the second year in order that the root system can fully develop.