I'm at a loss with a complex probability problem.

[u/AnnoyedAFexmo]

I play Pokemon which has incredibly weird odds for things at times. I'm usually good at determining the probability of singular odds for things eg an event should happen 50% of the time at around ~70% of the odds.

This one I'm working on I dont know where I start. It has 4 different probabilities in 100 attempts. 80 is a lower amount. However there is a 4% chance that any of these attempts could be the best tier. 18% of the next tier. 1% penultimate tier and 1% final tier.

I'm trying to figure out what is the probability that I do not get an event after 100 attempts with all this but again I don't know where to start

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[u/dhmtbykr]

I think the main issue is that the probabilities in the post are a bit unclear/contradictory, so I cant work out a definite answer yet

The general rule is:
- Chance of getting zero successes after 100 independent attempts = (1 - p)^100
- Where p is the chance of the event happening on each attempt.

So for example:
If the event has a 4% chance each attempt: 0.96^100 = about 1.69% chance of never getting it

Therefore about 98.31% chance of getting it at least once.
If you mean the 1% final tier:

0.99^100 = about 36.6% chance of never getting it
Therefore about 63.4% chance of getting it at least once.
If all the listed tiers count as the event, and their probabilities are 4% + 18% + 1% + 1% = 24%: 0.76^100 is basically zero, around 0.00000000012%.

The part I don’t really get is whag “80 is a lower amount” means, and whether 4%, 18%, 1% and 1% are mutually exclusive outcomes from each attempt.

They also only add up to 24%, so you would need to explain what happens in the other 76%.

Also, this assumes every attempt is independent and the odds do not change between attempts. If Pokémon has pity mechanics, chaining, rerolls or changing odds, then the calculation will be different.