Maths Puzzle - Probability of repeating event infinite times

The video presents a probability puzzle asking for the probability of an event occurring at least once in n attempts, given the probability of the event is 1/n. The solution involves defining a variable X and calculating the probability as 1 minus the probability of the event not occurring in n attempts. The video further explores the limit of this probability as n approaches infinity, revealing a connection to the numerical constant e. The instructor demonstrates algebraic manipulation to show that the limit is 1 - 1/e, approximately 0.632, highlighting the surprising emergence of e in this context.

What is the probability that an event with a probability of 1/n will occur at least once in n attempts?

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How is the variable X defined in the context of this probability puzzle?

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Explain the relationship between the probability of an event occurring at least once and the probability of it not occurring at all.

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What happens to the probability of the event occurring at least once as n approaches infinity?

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What is the significance of the numerical constant e in this probability puzzle?

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Describe the algebraic manipulation used to evaluate the probability as n approaches infinity.

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What is the approximate value of the limit of the probability that the event occurs at least once as n approaches infinity?

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