Question

‌A‌ ‌dice‌ ‌is‌ ‌rolled‌ ‌once.‌ ‌Find‌ ‌the‌ ‌probability‌ ‌of‌ ‌getting‌ ‌the‌ ‌number‌ ‌$5$‌ ‌

Answer 1

Hint: In this question, it is given that if a die is rolled once, then what the probability of getting the number $5$ is. So, for this we need to know the expression of probability which is,
\[\text{Probability}\left( P \right)=\dfrac{\text{The number of favourable outcomes}}{\text{Total number of possible outcomes}}\]
So, from the given data, we have to find all the possible outcomes and all the favourable outcomes and then find the probability accordingly.

Complete step-by-step solution:
As we know, a die is a six-sided cube with the numbers 1-6 placed on the faces. So from here we can say that if we throw a die then among these six faces one face must occur. Therefore,
\[\text{Total number of possible outcomes}=\text{ }6\]
Now the favourable outcome is to get the number $5$ , so between 1 to 6 there is only one such occurrence of $5$ . So,
\[\text{The number of favourable outcomes}=1\]
Therefore, we can say that,
\[\begin{align}
  & \text{Probability}\left( P \right)=\dfrac{\text{The number of favourable outcomes}}{\text{Total number of possible outcomes}}\\
 & \Rightarrow P=\dfrac{1}{6} \\
\end{align}\]
Thus, we can conclude that the probability of getting the number $5$ is $\dfrac{1}{6}$ .

Note: For solving these types of problems, we must be well aware about the definition of probability. We can express the probability as a decimal instead of a fraction. Also, we should remember to express the probability in the simplest form if we want to express it as a fraction. We should also be knowledgeable enough to know some basic theorems of probability like the total probability theorem, the Bayes theorem and so on. We should remember that the value of any probability must lie between two limits $0$ and $1$ .