A game spinner has regions that are numbered 1 through 8. If the spinner is used twice, what is the probability that the first number is a 3 and the second is a 5?
There are 8 possible outcomes for the first spin, since there are 8 regions numbered 1 through 8. Since we want the first number to be a 3, there is 1 favorable outcome: spinning a 3.
After the first spin, there are 8 possible outcomes for the second spin. We want the second number to be a 5, so there is 1 favorable outcome: spinning a 5.
Since each spin is independent of the other, we can multiply the probabilities. The probability of spinning a 3 on the first spin is $\dfrac{1}{8}$, and the probability of spinning a 5 on the second spin is $\dfrac{1}{8}$. Multiplying these probabilities gives $\dfrac{1}{8} \cdot \dfrac{1}{8} = \boxed{\dfrac{1}{64}}$.