Question

A die is rolled. Find the probability of getting a cube number.

Answer 1

Hint: When a die is rolled, we can have any number out of the numbers 1, 2, 3, 4, 5, and 6.
The possible outcomes when a die is thrown is {1, 2, 3, 4, 5, 6}. So, the total number of possible outcomes of a die 6. Therefore, the sample space is 6. We can see that the only perfect cube number from 1 to 6 is 1. So, the number of favorable outcomes is 1. We know the formula, \[\text{Probability=}\dfrac{\text{Number of favorable outcomes}}{\text{Total sample space}}\] . Now, use this formula and calculate the probability.

Complete step-by-step answer:
According to the question, it is given that we have a die that is rolled and we have to find the probability of getting a cube number.
We know that there are six faces of a die. So, whenever the die is rolled we can have any of the six faces. The faces of a die can have any number out of the numbers 1, 2, 3, 4, 5, and 6.
The possible outcomes when a die is thrown is {1, 2, 3, 4, 5, 6}. Therefore, the total number of possible outcomes of a die 6. Since the sample space of an event is the total number of the possible outcomes so, the sample space of this event is 6.
The total sample space = 6 ……………………(1)
Now, we have to get the number of favorable outcomes for a perfect cube number out of {1, 2, 3, 4, 5, 6}. We can see that the only perfect cube number from 1 to 6 is 1.
So, the number of favorable outcomes is 1 ……………………………..(2)
We know the formula, \[\text{Probability=}\dfrac{\text{Number of favorable outcomes}}{\text{Total sample space}}\] ………………………………(3)
Now, putting the values of sample space from equation (1) and the number of favorable outcomes from equation (2), in the formula shown in equation (3), we get
\[\text{Probability=}\dfrac{1}{6}\] .
Therefore, the probability of getting a cube number is \[\dfrac{1}{6}\] .

Note: In this question, one might take the number of possible outcomes for a perfect cube number as the sample space. This is wrong because the sample space of an event is the total number of the possible outcomes and here the possible outcomes are {1, 2, 3, 4, 5, 6}. Therefore, the sample space is 6.