Describe the Distribution's Two Properties

A discrete random variable ${\displaystyle x}$ takes a set of separate values (such as ${\displaystyle 0}$, ${\displaystyle 1}$, ${\displaystyle 2}$...). Its probability distribution assigns a probability ${\displaystyle P\left(x\right)}$ to each possible value ${\displaystyle x}$. For each ${\displaystyle x}$, the probability ${\displaystyle P\left(x\right)}$ falls between ${\displaystyle 0}$ and ${\displaystyle 1}$ inclusive and the sum of the probabilities for all the possible ${\displaystyle x}$ values equals to ${\displaystyle 1}$.

${\displaystyle 0.4}$ is between ${\displaystyle 0}$ and ${\displaystyle 1}$ inclusive, which meets the first property of the probability distribution.

${\displaystyle 0.1}$ is between ${\displaystyle 0}$ and ${\displaystyle 1}$ inclusive, which meets the first property of the probability distribution.

${\displaystyle 0.2}$ is between ${\displaystyle 0}$ and ${\displaystyle 1}$ inclusive, which meets the first property of the probability distribution.

${\displaystyle 0.1}$ is between ${\displaystyle 0}$ and ${\displaystyle 1}$ inclusive, which meets the first property of the probability distribution.

${\displaystyle 0.2}$ is between ${\displaystyle 0}$ and ${\displaystyle 1}$ inclusive, which meets the first property of the probability distribution.

For each ${\displaystyle x}$, the probability ${\displaystyle P\left(x\right)}$ falls between ${\displaystyle 0}$ and ${\displaystyle 1}$ inclusive, which meets the first property of the probability distribution.

Find the sum of the probabilities for all the possible ${\displaystyle x}$ values.