Probability Question with 2 rolls

Question

I have a probability question.

Say that there is a 2% chance of something occuring and then a 1d5 (20%) of it being a critical success.

So technically its a 0.4% chance of a critical success.

If we have more rolls, say 100 rolls. Would it still be a 0.4% for a critical success or would you have a higher chance?

Answer 1

For independent rolls, the chance of no critical success is the chance of not getting critical success on one roll, times $100$:

$P_0 = (1 - 0.004)^{100}=0.996^{100} \doteq 0.6698.$

Then, the probability of getting critical success on at least one roll of a hundred is

$P_{>0} = 1 - 0.996^{100} \doteq 0.3302,$

or about $1/3$.