If one person throws 100 times a fair dice with 100 corners (numbered from 1 to 100), then their probability to roll 100 at least once in any of those times equals:
$$P(X=100)=1-\left(\frac{99}{100}\right)^{100}\approx 0.63$$
Two scenarios:
A) Does it mean that if 100 people threw 1 time D100, we would expect with $63$% chance that at least one dice landed on 100?
B) Now, suppose we have 101 people. First 100 people throw D100 once, then the last person throws their own D100. This is repeated for 100 times. Do I understand correctly that regardless whether the first 100 people rolled 100 during their throw, the probability of the last person to roll 100 would still be $0.63$?
I'm expecting yes for both A) and B). Thank you.
A) Yes. It doesn't matter if 1 person throws a die 100 times or if 100 people throw a die 1 time, or of 50 people throw a die twice, they are all essentially identical ways of generating 100 independent, identically distributed (IID) dice rolls.
B) Yes. The last person throws their die 100 times. This is the same as any other way of generating 100 IID dice rolls. Among any collection of 100 fair IID D100 dice rolls, no matter who rolled them, or when, or for what purpose, there is a 63% chance of at least one being a 100.