Question

Two uniform dice marked 1 to 6 are thrown together. The probability that the sum is even is

• A. $\frac{1}{4}$
• B. $\frac{1}{3}$
• C. $\frac{1}{2}$
• D. $\frac{1}{12}$

Answer 1

The correct option is C $\frac{1}{2}$

Total cases when two dice are thrown $=6\times 6=36$
The sum would be even when both dice show either even or odd.
When both shows even numbers: 2, 4, 6,
So cases when dice show even numbers on both dice $=3\times 3=9$
When both shows odd numbers: 1, 3, 5.
So cases when dice show odd numbers on both dice $=3\times 3=9$
Total cases when sum of both dice is even $=9+9=18$
Probability when sum of both dice is even$=\frac{18}{36}=\frac{1}{2}$