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jmc

counting and probability junior

Problem

A board game spinner is divided into four regions labeled , , , and . The probability of the arrow stopping on region is , the probability of it stopping in is , and the probability of it stopping in region is equal to the probability of it stopping in region . What is the probability of the arrow stopping in region ? Express your answer as a common fraction.
Solution
Let be the probability that we want. Since the sum of the four probabilities is 1, we have the equation . Solving the equation gives .
Final answer
\frac{3}{16}