A board game spinner is divided into four regions labeled $A$, $B$, $C$, and $D$.  The probability of the arrow stopping on region $A$ is $\frac{3}{8}$, the probability of it stopping in $B$ is $\frac{1}{4}$, and the probability of it stopping in region $C$ is equal to the probability of it stopping in region $D$. What is the probability of the arrow stopping in region $C$?  Express your answer as a common fraction.
Let $x$ be the probability that we want. Since the sum of the four probabilities is 1, we have the equation $1 = \frac{3}{8} + \frac{1}{4} + x + x = \frac{5}{8} + 2x$.  Solving the equation $1=\frac{5}{8} + 2x$ gives $x=\boxed{\frac{3}{16}}$.
\frac{3}{16}
Level 2
Counting & Probability
Problem: A board game spinner is divided into four regions labeled $A$, $B$, $C$, and $D$.  The probability of the arrow stopping on region $A$ is $\frac{3}{8}$, the probability of it stopping in $B$ is $\frac{1}{4}$, and the probability of it stopping in region $C$ is equal to the probability of it stopping in region $D$. What is the probability of the arrow stopping in region $C$?  Express your answer as a common fraction.
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the probability of the arrow stopping in region C, we first need to understand that the total probability of all outcomes must equal 1. The probabilities of regions A, B, C, and D can be expressed as follows:

Let P(A) = 3/8, P(B) = 1/4, P(C) = x, and P(D) = x, since the probabilities of C and D are equal.

Next, we convert P(B) into a fraction with a common denominator to facilitate addition. The fraction 1/4 can be rewritten as 2/8. 

Now, we can set up the equation for the total probability:

P(A) + P(B) + P(C) + P(D) = 1
(3/8) + (2/8) + x + x = 1

Combining the known probabilities gives us:

(3/8) + (2/8) + 2x = 1
(5/8) + 2x = 1

To isolate 2x, we subtract 5/8 from both sides:

2x = 1 - (5/8)
2x = (8/8) - (5/8)
2x = 3/8

Now, we divide both sides by 2 to solve for x:

x = (3/8) / 2
x = 3/16

Thus, the probability of the arrow stopping in region C, which is equal to x, is 3/16. This leads us to conclude that the final answer is 3/16.<|END_OF_LATENT|> The final answer is $\frac{3}{16}$.