An unbiased six-sided die is rolled once. What is the probability that the number obtained is a multiple of 3?

Introduction / Context:
This question is a straightforward example of probability with a single fair die. It asks for the probability that the outcome is a multiple of 3. Such problems help reinforce counting favourable outcomes and dividing by the total number of equally likely outcomes.

Given Data / Assumptions:

• An unbiased six-sided die has faces numbered 1, 2, 3, 4, 5, 6.
• Each face is equally likely to appear on a single roll.
• We want the probability that the result is a multiple of 3.

Concept / Approach:
A multiple of 3 among the numbers 1 to 6 is any number that is divisible by 3 without remainder. We list such numbers in the set {1, 2, 3, 4, 5, 6}, count them, and then divide by 6, which is the total number of possible outcomes.

Step-by-Step Solution:
Possible outcomes on a six-sided die are: 1, 2, 3, 4, 5, 6. Multiples of 3 in this set are: 3 and 6. Number of favourable outcomes = 2 (namely 3 and 6). Total number of possible outcomes = 6. Required probability = favourable outcomes / total outcomes = 2 / 6. Simplify 2 / 6 by dividing numerator and denominator by 2 to get 1 / 3.

Verification / Alternative check:
We can check verbally: in one roll, there is a one third chance to land on 3 or 6, since there are two favourable faces out of six total. This informal reasoning matches the fraction 1/3, confirming the calculation.

Why Other Options Are Wrong:
1/6: This would correspond to only one favourable outcome, but there are actually two multiples of 3.
5/6: This would imply that only one face is not a multiple of 3, which is clearly incorrect for the numbers 1 to 6.
1/2: This suggests three favourable outcomes, but there are only two.
None of these: This is incorrect since 1/3 is a valid and correct option given in the list.

Common Pitfalls:
Some learners mistakenly treat 0 as a possible outcome on a standard die, which it is not. Others may miscount the multiples of 3 or forget to simplify the fraction 2/6. Always list the set of outcomes explicitly if there is any doubt, and remember to reduce the final fraction to its simplest form where possible.

Final Answer:
Therefore, the probability that the outcome is a multiple of 3 is 1/3.