Maybe it's like asking whether we choose our bodies, or our mother tongues or our homeland. Some beliefs are completely inaccessible to us, others are natural, but this changes with time. And what we make of them, whether we fight them or fashion something completely new with them, is not at all given.

My interpretation is that: we select amongst the options provided by our familial and cultural milieux. The manner in which we describe a person to another as yet unmet person reveals the significance of such milieux: "He comes from a wealthy, third generation, banking family in Northern Massachuchets, ......." says volumes about the "belief options" available and options not available to this person's development. A person born in India to a middle class Hindu family is quite unlikely have the same belief options available to them as a person born to a middle class Amrican southern Baptist bible class group leader. I believe that our DNA determines how we interpret our options and our familial taught values substantiate our order of prioritizing (determination of the order of urgency) of the application of our beliefs. 

emily's and james' response lead me to ask: do you believe that we can know some, none or all of our beliefs? can others point to beliefs we
have that till told we were unaware of? how much are our beliefs like water is to fish?