Sickle-cell disease is a hereditary medical condition affecting red blood cells. Some forms are benign, but other forms cause health problems leading to reduced life expectancy. Sickle-cell appears to protect against malaria, which may explain why it comes from tropical sub-Saharan Africa where malaria is endemic. A group of African children were tested for both sickle-cell and malaria. Out of the whole group, 23% had sickle-cell, 35% had malaria, and 6% had both.

(a) Use a contingency table to structure the above information about the incidence of sickle- cell and malaria among these children. Complete all marginal totals as well as the body of the table. [4]

(b) What proportion of children with malaria also had sickle-cell? [2]

(c) Among children who had sickle-cell, what proportion did not have malaria? [2]

(d) Among the children tested, is having malaria statistically independent of having sickle-cell? Justify your answer.