Question

What is the probability of rolling a number cube and it landing on the number 3?

Answer 1

Hint: We are asked to find the probability of rolling a number cube and it landing on the particular number. We can solve such probability based problems by defining a proper sample space for the situation and then calculating the probability by dividing required outcomes by the total number of outcomes in the sample space or the sample set.

Complete step by step solution:
The number for which we need to find the probability of landing is 3. First, assuming that we have a fair cube or die, we have to define a sample space for the underlying problem. The sample space is the set containing all the possible outcomes for the given situation. We know that for a fair die, the chances of landing on all 6 faces are the same and there are 6 distinct outcomes possible. That is,
$S=\left\{ 1,2,3,4,5,6 \right\}$
We also know that, by the law of probability, the total probability for any event must be equal to one. Hence, we have 6 outcomes here which are equally likely and their probabilities would be equal to $\dfrac{1}{6}$ .
Finally, we can find the required probability by finding the ratio of desired outcome to total outcomes. Since 3 is the desired outcome and there are 6 outcomes in total, we can conclude that the probability of rolling a number cube and landing on the number 3 is $\dfrac{1}{6}$.

Note: We have assumed the fact that all outcomes are equally likely or in other words, that we have a fair die. This may not always be the case and we may have a biased die as well, in such a case we will have unequal probabilities for each outcome and we must choose the required probability value carefully.