In a TV game show, four prizes are hidden on a game board that contains 20 spaces.

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In a TV game show, four prizes are hidden on a game board that contains 20 spaces. One prize is worth \(\$ 10,000\), two prizes are worth \(\$ 5,000\), and the other prize is worth \(\$ 1,000\). The remaining spaces contain no prizes. The game show host offers a sure prize of \(\$ 1,000\) not to play this game. Should the contestant choose the sure prize or play the game?

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