$\"\"$

\

The random variable is $\"\"$ .

\

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

\

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

\

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

\

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

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

The geometric series is $\"\"$ .

\

Convergence of a geometric series:

\

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

\

$\"\"$

\

Therefore, $\"\"$ .

\

$\"\"$

\

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

\

$\"\"$ .