Question

A Dice is thrown. Probability of getting an even number is ____.

• A. 1/6
• B. 1/3
• C. 1/2
• D. 2/3

Hint:

On a standard 6-sided die, exactly half the numbers are even (2, 4, 6) and half are odd (1, 3, 5). Therefore, the probability for either event is always 0.5 or 1/2.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Probability is the ratio of the number of favorable outcomes to the total number of possible outcomes in a random experiment.

Step 2: Key Formula or Approach:
\[ P(E) = \frac{n(E)}{n(S)} \] Where $n(E)$ is the number of favorable outcomes and $n(S)$ is the total number of outcomes in the sample space.

Step 3: Detailed Explanation:
1. Total outcomes when a die is thrown: \( S = \{1, 2, 3, 4, 5, 6\} \). So, \( n(S) = 6 \). 2. Favorable outcomes (even numbers): \( E = \{2, 4, 6\} \). So, \( n(E) = 3 \). 3. Probability: \[ P(\text{Even}) = \frac{3}{6} = \frac{1}{2} \]

Step 4: Final Answer:
The probability of getting an even number is 1/2.

Answer 2

Instead of directly counting favourable outcomes, we can use the complement rule: the probability of getting an even number plus the probability of getting an odd number must add up to 1, since every face of a standard die is either odd or even.

1. 1/6: This is the probability of landing on any one specific number, for example just a 4. It severely understates the chance of getting any even number at all, since there are three even faces, not one.
2. 1/3: This would result from mistakenly treating only two of the three even faces as favourable outcomes, for example counting just \( \{2, 4\} \) instead of all of \( \{2, 4, 6\} \).
3. 1/2: On a standard die, the faces split evenly into three odd numbers \( \{1, 3, 5\} \) and three even numbers \( \{2, 4, 6\} \). Since these two sets are equally sized and exhaustive, \( P(\text{even}) = P(\text{odd}) \), and since they must add to 1, each must equal \( \frac{1}{2} \).
4. 2/3: This would result from over-counting, for instance including a number that is neither odd nor even, or double counting one of the even faces. A standard die has exactly three even faces out of six, not four.

Because the odd and even outcomes split the die exactly in half, the probability of either one is one-half.

Therefore, the correct answer is 1/2.