Probability of Rolls (Math Question) (200k Prize)

[Regalmurk]

I said in All-Chat Silver
That if I've 10k Encounters my chances of seeing AT LEAST one shiny will be around 70% not ~1/9k whatever the shiny rate is. This seems like simple maths to me. Rolling at least 1 Heads is VERY LIKELY in 10 coins flips, it's not 50%. But then a player started to attack me saying I'm spreading misinformation, I'm dumb, I'm noob. Well I'm noob in the game haha it's true.

Maybe I'm missing something? All the players online seemed to agree with him but when I asked explanation they kept spamming the same thing that it's independent chance. I'm talking about a set of events though not the next encounter as independent.

I'm no mathematician (even though I'm a programmer lol) so I'm not 100% sure myself lol. I just feel it's conditional probability simple stuff studied in school.  https://www.youtube.com/watch?v=98TQv5IAtY8 This is the video I watched when I was young to have this idea.

It's interested. I'm pretty sure I'm right but why do people not get it? Any opinions on this I would appreciate just no toxicity please. There is a chance I'm wrong. But if I'm not people why are people so confident that they are right that I'm wrong and this is misinformation.

Topic is interesting , we play game of probability only so I feel this is an interesting topic. 

I will pick the first person who I feel cleared my doubts and give them 200k as well  Because I've money I don't know where to spend haha. I won't do favourites coz I know almost nobody in this community. Discussion can keep going if interested although I doubt math stuff is very popular here.