Pretty much everything that we use probability to model has underlying causes and reasons, if we could only detect and measure them (at least until you get down to quantum mechanics), but probability can still be a useful way to model problems where either we don't fully understand the underlying causes, or the underlying causes are just too complicated and tangled to directly model.
There are over 200 different types of cancer. Not all of these are caused by contact with carcinogens. So, for these cancers it's pretty much "luck" whether you get them or not. Not smoking; sensible drinking; etc will not prevet you from getting them.
However, we are aware of quite a few known, and many probable, carcinogens.[1][2] Among women, breast cancer comprises 60% of alcohol-attributable cancers.[3] And to support the claim that certain foods, when prepared in certain ways, can become carcinogenic take a look at the research on Heterocyclic amines,[4] and acrylamide.[5]
1. http://www.cancer.org/cancer/cancercauses/othercarcinogens/g...
2. http://en.wikipedia.org/wiki/List_of_IARC_Group_1_carcinogen...
3. http://onlinelibrary.wiley.com/doi/10.1002/ijc.21903/abstrac...
4. http://en.wikipedia.org/wiki/Heterocyclic_amine#Heterocyclic...
5. http://en.wikipedia.org/wiki/Acrylamide#Toxicity_and_carcino...
If repeated studies show strong associations, like say between cigarettes and cancer, it would make sense to take some steps to prevent the potential cause.