Here is my question:
Imagine that on a $6$-sided die, each die that lands on $4$ or less counts as a hit. Each time you roll all four dice in your dice pool at once, you want to get at least three hits. What is the probability of that happening?
I have some ideas, but I'm not totally sure if they make sense, they're just intuition. It's not a straight probability like $(\frac{2}{3})^4$ because only three need to hit, but it's not raised to the $3^{rd}$ either because you have that extra die. The best I could come up with is $\frac{2+2+2+3}{3\cdot{4}}=\frac{9}{12}=0.75$, but I can't think of how to back that up with a proof. Any ideas?