Question

What is the probability distribution of rolling a single die?

Answer 1

Hint: In order to find the probability distribution of rolling a single die, we have to consider all the possible outcomes. There would be a total of six possible outcomes as a die has six faces and all should be considered. All the outcomes would be independent outcomes.

Complete step by step solution:
Now let us learn about the probability. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. There are three major types of probabilities: Theoretical Probability. Experimental Probability, Axiomatic Probability. Probabilities can be expressed in percentages ranging from \[0%\] to \[100%\].
Now let us find out the probability distribution of rolling a single die.
We know that we would obtain six independent outcomes and they are \[1,2,3,4,5,6\].
Now we will be calculating the probability of each outcome.
\[\begin{align}
  & P\left( 1 \right)=\dfrac{1}{6} \\
 & P\left( 2 \right)=\dfrac{1}{6} \\
 & P\left( 3 \right)=\dfrac{1}{6} \\
 & P\left( 4 \right)=\dfrac{1}{6} \\
 & P\left( 5 \right)=\dfrac{1}{6} \\
 & P\left( 6 \right)=\dfrac{1}{6} \\
\end{align}\]

\[\therefore \] They have equal probabilities as the dice is not biased.

Note:
The sum of probabilities is always one. There are three main rules associated with basic probability. They are the addition rule, the multiplication rule and the complement rule. We can give an outcome a probability of 0 if we are sure that that outcome will never occur. Likewise, if we assign a probability of 1 to an event, then that event must occur all the time.