Question

What is the probability of rolling a $4$ on a number cube?

Answer 1

In this question, we have to find the probability of getting $4$ on a number cube i.e., die.
We know, a die has a total of $6$outcomes, so, the sample space becomes = \left\\{ {1,2,3,4,5,6} \right\\} . So, in this, we’ll find the total number of outcomes and the number of favorable outcomes and divide them to get the probability.
The simple formula that we know of probability is given by $\dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Total number of outcomes}}}}$ .

Complete step by step solution:
Given the outcome we want is $4$ .
We know, the total number of outcomes in a die is $6$ which are numbers from one to six, so, when we throw this die, then we’ll get the one outcome out of these six numbers only.
So, the Sample space becomes \left\\{ {1,2,3,4,5,6} \right\\} .
So, the total number of outcomes $= 6$ , out of which we need to find the probability of getting $4$ .
Since, the occurrence of$4$ is only once, therefore, the number of favorable outcomes is only one.
Now, to get the probability we will divide the number of favorable outcomes by the total number of outcomes i.e., the probability is given by $\dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Total number of outcomes}}}}$ .
Hence, the probability of getting $4$ becomes $= \dfrac{1}{6}$ .

Note: Here, we have assumed that each outcome of the rolling cube is equally likely. i.e., a fair die. Otherwise, our solution will be different.
If we don’t have a fair die, the number of favorable outcomes will be changed, according to the given outcomes.
For solving such problems, one must be aware of the definition and the basic properties of probability i.e., probability always lies between $0$ and $1$ . Also, remember to express the probability into the lowest form.