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Omni-MATH / You have infinitely many boxes, and you randomly put 3 balls into them. The…

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problem

You have infinitely many boxes, and you randomly put 3 balls into them. The boxes are labeled 1,2,…1,2, \ldots. Each ball has probability 1/2n1 / 2^{n} of being put into box nn. The balls are placed independently of each other. What is the probability that some box will contain at least 2 balls?
Plain-text mathematical notation (without MathML)
You have infinitely many boxes, and you randomly put 3 balls into them. The boxes are labeled 1,2,…. Each ball has probability 1/2^(n) of being put into box n. The balls are placed independently of each other. What is the probability that some box will contain at least 2 balls?
Original LaTeX notation
You have infinitely many boxes, and you randomly put 3 balls into them. The boxes are labeled $1,2, \ldots$. Each ball has probability $1 / 2^{n}$ of being put into box $n$. The balls are placed independently of each other. What is the probability that some box will contain at least 2 balls?

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Source and history

task_id
1abbc5ed-6863-5794-9060-f86062579a22
task_key
test--1abbc5ed-6863-5794-9060-f86062579a22
task_revision_id
1
config / split
/ test

Official source

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