$\"\"$

The random variable is $\"\"$ .

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

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

$\"\"$ .

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

$\"\"$

The geomentric series is $\"\"$ .

Convergence of a geomentric series:

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

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

$\"\"$

Therefore, $\"\"$ .

$\"\"$

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

$\"\"$ .