Say you have two 5-sided dice. What is the probability of rolling these dice together, and getting exactly one even number? Hint: You may want to write out the sample space. (answer in fractions)

To find the probability of rolling two 5-sided dice and getting exactly one even number, we first need to determine the sample space.

The sample space is the set of all possible outcomes when rolling two 5-sided dice. Let's label the dice as dice A and dice B. Since each die has 5 sides, the possible outcomes for each die are 1, 2, 3, 4, and 5. Therefore, the sample space consists of all possible pairs of outcomes, denoted as (A, B), where A represents an outcome of dice A and B represents an outcome of dice B.

The sample space is:
\{(1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (2,5), (3,1), (3,2), (3,3),\ (3,4), (3,5), (4,1), (4,2), (4,3), (4,4), (4,5), (5,1), (5,2), (5,3), (5,4),\ (5,5)\}

To calculate the number of outcomes in the sample space, we count that there are 5 possible outcomes for dice A and 5 possible outcomes for dice B, giving a total of 25 outcomes.

Now we need to determine the favorable outcomes, i.e., the outcomes where exactly one even number is rolled.

From the sample space, we can see that the favorable outcomes consist of pairs where one die is even and the other is odd. So, the favorable outcomes are:
\{(1,2), (1,4), (2,1), (2,3), (2,5), (3,2), (4,1), (4,3), (4,5), (5,2)\}

Counting the favorable outcomes, we see that there are 10 such outcomes.

Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of outcomes in the sample space:

\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}

Therefore, the probability of rolling two 5-sided dice and getting exactly one even number is:

\text{Probability} = \frac{10}{25}

Simplifying the fraction, we get:

\boxed{\text{Probability} = \frac{2}{5}}