1. **Problem statement:** Find the probability that a student passes the statistics test given: - Probability to pass math test $P(M) = \frac{2}{3}$ - Probability to pass both math and statistics tests $P(M \cap S) = \frac{14}{45}$ - Probability to pass at least one test $P(M \cup S) = \frac{7}{9}$ 2. **Formula used:** The formula for the union of two events is: $$P(M \cup S) = P(M) + P(S) - P(M \cap S)$$ 3. **Step-by-step solution:** Using the formula, substitute the known values: $$\frac{7}{9} = \frac{2}{3} + P(S) - \frac{14}{45}$$ 4. **Simplify the equation:** Convert all fractions to have a common denominator 45: $$\frac{7}{9} = \frac{35}{45}, \quad \frac{2}{3} = \frac{30}{45}$$ So, $$\frac{35}{45} = \frac{30}{45} + P(S) - \frac{14}{45}$$ 5. **Isolate $P(S)$:** $$P(S) = \frac{35}{45} - \frac{30}{45} + \frac{14}{45}$$ 6. **Calculate $P(S)$:** $$P(S) = \frac{35 - 30 + 14}{45} = \frac{19}{45}$$ **Final answer:** The probability that the student passes the statistics test is $\boxed{\frac{19}{45}}$.