Consider a family with a mother, father, and two children. Let A, = {mother has influenza}, A, = {father has influenza}, A, = {first child has influenza}, A, = {second child has influ- enza}, B= {at least one child has influenza}, C= {at least one parent has influenza}, and D = {at least one person in the family has influenza}. *3.1 What does A, UA, mean? *3.2 What does A, nA, mean? *3.3 Are A, and A, mutually exclusive? *3.4 What does A, UB mean? *3.5 What does A, nB mean? *3.6 Express C in terms of A,, A,, A and A.. *3.7 Express D in terms of B and C. *3.8 What does Ā, mean? *3.9 What does Ā, mean? *3.10 Represent Cin terms of A,, A,, A, and A,. *3.11 Represent D in terms of B and C. Suppose an influenza epidemic strikes a city. In 10% of families the mother has influenza; in 10% of families the father has influenza; and in 2% of families both the mother and father have influenza. 3.12 Are the events A, = {mother has influenza} and A, = {father has influenza} independent? Suppose there is a 20% chance each child will get influ- enza, whereas in 10% of two-child families both children get the disease. 3.13 What is the probability that at least one child will get influenza? 3.14 Based on Problem 3.12, what is the conditional prob- ability that the father has influenza given that the mother has influenza? 3.15 Based on Problem 3.12, what is the conditional prob- ability that the father has influenza given that the mother does not have influenza?