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Omni-MATH / On a game show, Merble will be presented with a series of 2013 marbles, each of…

Problem

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problem

On a game show, Merble will be presented with a series of 2013 marbles, each of which is either red or blue on the outside. Each time he sees a marble, he can either keep it or pass, but cannot return to a previous marble; he receives 3 points for keeping a red marble, loses 2 points for keeping a blue marble, and gains 0 points for passing. All distributions of colors are equally likely and Merble can only see the color of his current marble. If his goal is to end with exactly one point and he plays optimally, what is the probability that he fails?

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Source and history

task_id
9a8b6a72-d3ec-566a-b2dd-98f6fc1695f8
task_key
test--9a8b6a72-d3ec-566a-b2dd-98f6fc1695f8
task_revision_id
1
config / split
/ test

Official source

initial import