Nope, it's not about the number of mutations you get. It's also about the repair mecanisms of your DNA not working as well anymore. That's why cancer occurs more frequently with aging.

I forgot the actual source link, but I remember seeing a publication showing how autopsies on young people who died of accidental circumstances showed tiny cancer tumors in their bodies even in their 20s-30s, and that simply these would not grow further because of the repair mechanisms being highly effective in younger organisms.

So basically you get mutations in your body the whole time. Not just when you age.