Question: An evil scientist has devised an experiment that takes one hour to run to completion. It has a 1/12 chance of causing the world to

An evil scientist has devised an experiment that takes one hour to run to completion. It has a 1/12 chance of causing the world to explode. Otherwise, it fails and the evil scientist immediately resets the experiment and tries again! (Her attempts are independent and each has probability 1/12 of succeeding.) Knowing that a nearby hero will find the evil scientist and foil her plan after 8 hours have passed, what is the probability that the evil scientist will succeed before the hero catches her, i.e., that the evil scientist will have a success within her first 8 attempts?

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