Two cubes with the faces numbered 1 through 6 are tossed and the numbers shown on the top faces are added. What is the probability that the sum is even? Express your answer as a common fraction.
+998 There are two ways that we can end up with an even number by adding two numbers.
Either both numbers have to be even, or both have to be odd.
Starting off, let's find out the probability that we will roll two cubes and they will both show an even number.
For cube A, we have \(6\) possible outcomes. Out of those six, three numbers are even (\(2 , 4, 6\)).
Therefore, we have \(\frac{3}{6} = \frac{1}{2}\) ways to roll one cube and have an even number show up.
This is the same for cube B. In total, we have \(\frac{1}{2} * \frac{1}{2} = \frac{1}{4}\) ways to roll two cubes and have both of them show even numbers.
If we do the same thing for the odd numbers, we would get the same result of \(\frac{1}{4}\).
Adding these two possibilities together, we would get \(\frac{1}{4} + \frac{1}{4} = \frac{1}{2}\)
Therefore, our answer is \(\boxed{\frac{1}{2}}\)
+127 Well,
even + even == even, 3#s * 3#s == 9#s
and
odd + odd == even, 3#s*3#s == 9#s
and
there are 6*6 == 36, so therefore our answer is (9+9)/36 == 18/36 == 1/2
