I think this is an application of a negative Bernoulli distribution, Pascal form. But I'm not sure how to formulate it.
The Problem
In a game of MineCraft+ThaumCraft, you can burn found resources in a magic cauldron for a chance to create a special item. The chance for success is specified, and resources to burn for each trial require time and effort to go collect. There is overhead involved in going off to collect resources, so the objective is to collect enough resources to ensure at least one success.
Let's set the value of certainty to 95%, where 19/20 runs of the experiment go according to plan.
What I want to know is: Given the probability of success, p, on each independent trial, how many trials must be executed so that the chance of failure of all trials in the set is less than or equal to 5%?
The Problem
In a game of MineCraft+ThaumCraft, you can burn found resources in a magic cauldron for a chance to create a special item. The chance for success is specified, and resources to burn for each trial require time and effort to go collect. There is overhead involved in going off to collect resources, so the objective is to collect enough resources to ensure at least one success.
Let's set the value of certainty to 95%, where 19/20 runs of the experiment go according to plan.
What I want to know is: Given the probability of success, p, on each independent trial, how many trials must be executed so that the chance of failure of all trials in the set is less than or equal to 5%?