How many times do I have to try for winning something if my chances are 20%?
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It depends on if you’re talking dependent or independent probabilities.
If you have a 5-sided die, each time you roll there is a 20% chance it will land on a ‘1’. No matter how many times you roll it, the chance is still the same for the trial. To calculate the chance of getting some exact sequence of rolls involves some multiplication. A trivial example of this would be “what is the chance I don’t see a ‘1’ after n rolls?” – which is .8^n. This means you are never guaranteed to see a ‘1’ no matter how many times you roll.
On the other hand, if I have a jar with 4 red pebbles and 1 black pebble, the chance of drawing a black pebble is 20%. But if I’ve already drawn a red pebble, the chance of drawing a black pebble is now 25% (since there are only 3 red pebbles left out of 4 total pebbles). The probability of each subsequent trial is dependent on the trials that preceded it. If I draw 5 pebbles from that jar, it should be obvious that I’m guaranteed to get a black pebble.
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