$\"\"$

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The random variable is $\"\"$ .

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Where $\"\"$ represents the number of units of a product sold per day in a store.

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The probability of $\"\"$ is $\"\"$ .

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Calculate the probability $\"\"$ that $\"\"$ are sold in a day.

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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The geomentric series is $\"\"$ .

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Convergence of a geomentric series:

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A geomentric series with ratio $\"\"$ diverges if $\"\"$ , then series converges to the sum

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$\"\"$ .

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$\"\"$

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Therefore, $\"\"$ .

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$\"\"$

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The probability that $\"\"$ are sold in the day is $\"\"$ .

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$\"\"$ .