What is the chance of not inheriting *any* DNA from a particular grandparent?

This is a crazy, new idea to me.

I have always imagined DNA as a hash function, and grandparents DNAs a AND b yields your dad's: H(grandma, grandpa) = DNA, which means you will inherit this chain H(your dad, your mom) = yours). Now I am told that is not the case at all. So what DNA am I receiving? I am confused.