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Omni-MATH / A random number selector can only select one of the nine integers 1, 2, ..., 9,…

Problem

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problem

A random number selector can only select one of the nine integers 1, 2, ..., 9, and it makes these selections with equal probability. Determine the probability that after nn selections ( n>1n>1 ), the product of the nn numbers selected will be divisible by 10.
Plain-text mathematical notation (without MathML)
A random number selector can only select one of the nine integers 1, 2, ..., 9, and it makes these selections with equal probability. Determine the probability that after n selections ( n>1 ), the product of the n numbers selected will be divisible by 10.
Original LaTeX notation
A random number selector can only select one of the nine integers 1, 2, ..., 9, and it makes these selections with equal probability. Determine the probability that after $n$ selections ( $n>1$ ), the product of the $n$ numbers selected will be divisible by 10.

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Source and history

task_id
7e6a9af3-862f-5c23-bd9a-270c213f95e6
task_key
test--7e6a9af3-862f-5c23-bd9a-270c213f95e6
task_revision_id
1
config / split
/ test

Official source

initial import