$\"\"$

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The treasure chest is opened $\"\"$ times per game, so $\"\"$ .

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Open the chest and find gold coins exactly $\"\"$ times, so $\"\"$ .

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(a)

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Find the value of $\"\"$ .

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Substitute $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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(b) What is the probability that a person playing the game will find gold in the chest than 12 times.

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The probability that it contains gold coins is $\"\"$ , so $\"\"$ .

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The value of $\"\"$ .

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Open the chest and find gold coins more than $\"\"$ times, so $\"\"$ or $\"\"$ or $\"\"$ .

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Find the value of $\"\"$ .

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Substitute $\"\"$ , $\"\"$ and $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Substitute $\"\"$ , $\"\"$ and $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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Substitute $\"\"$ , $\"\"$ and $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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Therefore, the probability to geth the gold more than $\"\"$ times is

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$\"\"$ or $\"\"$ .

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$\"\"$

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(a) $\"\"$ .

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(b) The probability to geth the gold more than $\"\"$ times is $\"\"$ .