Originally Posted by

**ksdhart2**
From my perspective, it looks like your main problem isn't really that you're "bad at probability" or even bad at math. Rather, the problem is that you don't have a clearly defined problem. I'll be blunt and hope to not come off as rude, but your first paragraph in which you explained the problem you're trying to solve felt very much like a stream of consciousness, with no attempts to organize the thoughts in a cohesive manner. For instance, the goal of the problem, as I'm interpreting what you wrote, is the last sentence here:

Given this instruction, your answer that the probability is (6-y)/6 is absolutely correct. We can examine this in detail and see why this must be the case. Consider the very first dice roll, where you've not rolled any numbers so far. Obviously, any number you roll must be unique, so you have 100% probability. In this case, we have y = 0. Your answer would indicate that the probability is (6-0)/6 = 6/6 = 1 = 100%, so we're good. Now what if y = 1? You've rolled one unique number so far, that means there are 5 unique numbers out of the 6 total numbers remaining. Your answer says the probability is (6-1)/6 = 5/6, so we're good there too. Now what if y = 2? You've rolled two unique numbers so far, that means there are 4 unique numbers out of the 6 total numbers remaining. Your answer says the probability is (6-2)/6 = 4/6, so we're good there too. And so on...

However, from the fact that you then go on to say that "This [answer] failed on a few test cases," that I've misinterpreted the goal of the problem. At this point, it should be clear that before we can even begin to use any mathematical or probability principles to solve the problem, we have to know what the problem even is. So my best recommendation is that you try to collect your thoughts and better explain what it is you're trying to ask.

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