Forgive me if this has been answered, but I couldn't quite find what I'm looking for. Maybe I'm not used to the mathematical terms.
Say there is an event with a chance of 1 in 20 of being successful. This chance doesn't change in each trial.
If there were N trials (let's say 2 for a concrete example), then what is the chance of the next trial (N+1) being successful?
Trial 1: Fail
Trial 2: Fail
Trial 3: ?
Best Answer
This depends on how your trials are set up. Specifically whether they're independent or not. Look at two cases:
(There is a 1.5 where you picked out 19000000 black cards and 1000000 cards.) Note that in both cases, the probability of success on any specific trial is 1 in 20. But in the second case knowledge of the result of other trials changes the probability.