1. **State the problem:** Georgina surveys 25 people. 6 like hockey, 8 like rugby, and 16 like neither. We need to find the probability that a person who likes rugby also likes hockey. 2. **Understand the sets:** Let $H$ be the set of people who like hockey, $R$ the set who like rugby, and $N$ those who like neither. 3. **Given:** - Total people $= 25$ - $|H| = 6$ - $|R| = 8$ - $|N| = 16$ 4. **Find the number who like hockey or rugby or both:** $$|H \cup R| = 25 - 16 = 9$$ 5. **Use the formula for union:** $$|H \cup R| = |H| + |R| - |H \cap R|$$ Substitute known values: $$9 = 6 + 8 - |H \cap R|$$ 6. **Solve for intersection:** $$|H \cap R| = 6 + 8 - 9 = 5$$ 7. **Calculate the probability that a person who likes rugby also likes hockey:** This is the conditional probability: $$P(H|R) = \frac{|H \cap R|}{|R|} = \frac{5}{8}$$ **Final answer:** The probability that a person who likes rugby also likes hockey is $\frac{5}{8}$.