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It takes t amount of time for you to navigate the Gauntlet of Pain. The Gauntlet electrifies and shocks anyone on it at random intervals. The intervals between shocks are independently and identically distributed. Assume shocks are instantaneous. Obviously, you do not wish to be shocked. Picture an "opportunity" as a window of time (an interval between shocks) that is greater than or equal to time t, which allows you to run across the Gauntlet without being shocked. Also suppose the timeline begins directly after the last shock (shock number 0).

Imagine there are exactly m opportunities to cross safely by the time the nth shock occurs. What is the probability that the mth opportunity is a close call (that it occurs immediately before the nth shock).

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Statistics and Probability, Statistics

Category:- Statistics and Probability
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