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Balls and Boxes Puzzle

For simplicity, I’ll call them Box A and Box B. You should put one red ball in Box A and the rest of the balls in Box B.

There is a 50% chance the person will pick Box A, and a 100% chance they will pick the red ball if they do.

There is a 50% chance they will pick Box B, and about a 49.5% (49/99) chance they will pick the red ball if they do.

This distribution creates a 0.5 x 100 + 0.5 x 49.5 = 74.75% chance they will pick the red ball.

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