RNG percentage ratios based on completion time

Question

so theres 2 scenarios that can completed in the same

frame of time - but both have different (random number generator)

possible chances for a targeted reward

#1 - task that takes the whole block of time and

has a 1 out of 27,000 chance of wanted result

#2 - task that can be completed 3 times in the same

frame of time - and each has a 1 out of 30,000

chance of wanted result

so my question is what is the chance ratio for the second scenario

when you do all 3? because your doing 3 does that make the overall

chance for that time frame 1 out of 10,000 in comparison to the1 out of

27,00 for the first task when they are done in the same time frame?

that seems like the simple answer - but i dont know for sure

and would like to know the exact answer - thanks

Answer 1

If I understand correctly, in scenario 2 you are running the game (or experiment) 3 times.

Do you want the probability that you succeed exactly once, or at least once?. These are different.

Let p = 1/30000, q=1-p

P(exactly once) = 3*p*q² -- there are 3 ways it could happen each with Prob= p*q²

P(at least once) = 1 - P(none) = 1 - q³