Question

If a single 6-sided die is rolled, then what is the probability of rolling a 4 on the die?
(a) $\dfrac{1}{12}$,
(b) $\dfrac{2}{3}$,
(c) $\dfrac{3}{2}$,
(d) $\dfrac{1}{6}$.

Answer 1

We start solving the problem by recalling what are the numbers present in a 6-sided die. We then find the total number of possibilities of getting a number on rolling the die using the numbers present on the die. We then find the total number of favorable cases of getting 4 on rolling the die. We then take the ratio of total number of favorable cases to the total number of possibilities to get the required result.

Complete step-by-step answer:
According to the problem, we have a single 6-sided die and we need to find the probability of rolling a 4 on the die.
We know that there will be six numbers on a 6-sided die which are as follows: \left\\{ 1,2,3,4,5,6 \right\\}. When we roll this die, we have a chance that we can roll any one of these six numbers.
So, the total number of possibilities to get a number on rolling the die for one time is 6.
We need to find the probability of getting the number 4 on rolling this die.
We know that the probability of event is defined as $probability=\dfrac{total\ no. of\ favorable\ cases}{total\ no. of\ possibilities}$.
According to the problem, the favorable is getting 4 on rolling the die. From the total number of possibilities, we can see that there are only four that are present on the die. We have only a favorable case in a total of 6 possibilities.
So, the required probability = $\dfrac{1}{6}$.
So, we have found the probability of getting a 4 on rolling the single 6-sided die as $\dfrac{1}{6}$.
∴ The correct option for the given problem is (d).

So, the correct answer is “Option (d)”.

Note: We assumed that the given 6-sided die is not biased die. Whenever we get a problem involving rolling of dies, we assume the die as un-biases unless it is mentioned as biased. We should not take random numbers on the die as \left\\{ 1,2,3,4,5,6 \right\\} are the standard numbers present on any given die. Similarly, we can expect problems to find the probability of getting a number when a biased die is rolled.