Question

How do you determine the theoretical probability of rolling a five on a die?

Answer 1

This problem deals with finding the probability of an event, where the event is rolling a die and expecting a five. We know that the probability of an event is equal to the ratio of the outcome of a favorable outcome of an event occurring to the ratio of the total number of possible outcomes.

Complete step-by-step solution:
Here the given favorable outcome is that a dice should be able to roll the number five out of all possible six outcomes.
So the probability of every possible outcome of this dice is equal to $\dfrac{1}{6}$.
The probability of occurring 1 on the dice is given below:
$\Rightarrow P\left( 1 \right) = \dfrac{1}{6}$
The probability of occurring 2 on the dice is given below:
$\Rightarrow P\left( 2 \right) = \dfrac{1}{6}$
The probability of occurring 3 on the dice is given below:
$\Rightarrow P\left( 3 \right) = \dfrac{1}{6}$
The probability of occurring 4 on the dice is given below:
$\Rightarrow P\left( 4 \right) = \dfrac{1}{6}$
The probability of occurring 5 on the dice is given below:
$\Rightarrow P\left( 5 \right) = \dfrac{1}{6}$
The probability of occurring 6 on the dice is given below:
$\Rightarrow P\left( 6 \right) = \dfrac{1}{6}$
The theoretical probability of rolling a five on a die is equal to $\dfrac{1}{6}$.

Note: Please note that here we are asked to find the probability of an event of a fair dice. A dice has six faces, and each face has each number starting from 1 to 6. But in case of an unfair dice, then we have to consider all the possible conditions given in order to find the best result.