1. **State the problem:** We have a class of 30 students. 16 have black hair, 11 have brown eyes, and 7 have both black hair and brown eyes. We need to find the values A, B, C in the Venn diagram and calculate the probabilities of having black hair or brown eyes, and having neither. 2. **Identify the sets and intersection:** - Let A = number of students with black hair only. - Let B = number of students with both black hair and brown eyes. - Let C = number of students with brown eyes only. - Let D = number of students with neither black hair nor brown eyes. 3. **Use the given data:** - Total students $=30$ - Black hair total $=16$ - Brown eyes total $=11$ - Both black hair and brown eyes $=7$ 4. **Calculate A and C:** $$A = 16 - 7 = 9$$ $$C = 11 - 7 = 4$$ 5. **Calculate D (neither):** $$D = 30 - (A + B + C) = 30 - (9 + 7 + 4) = 30 - 20 = 10$$ 6. **Calculate probabilities:** - Probability of black hair or brown eyes is the union: $$P(Black\ Hair \cup Brown\ Eyes) = \frac{A + B + C}{30} = \frac{9 + 7 + 4}{30} = \frac{20}{30} = 0.7$$ - Probability of neither black hair nor brown eyes: $$P(neither) = \frac{D}{30} = \frac{10}{30} = 0.3$$ 7. **Round answers to 1 decimal place:** - $P(Black\ Hair \cup Brown\ Eyes) = 0.7$ - $P(neither) = 0.3$ **Final answers:** - $A=9$ - $B=7$ - $C=4$ - Probability(black hair or brown eyes) $=0.7$ - Probability(neither) $=0.3$