Consider a family with a mother, father, and two children. Consider the following set of events: A1={mother has influenza}; A2={father has influenza}; A3={first childhas influenza}; A4={second child has influenza}; B={at least one childhas influenza}; C={at least one parent has influenza}; D={at least one family memberhasinfluenza}. What does A1 A2mean?

(a) Either the mother or the father has influenza (b) Both the mother and the father have influenza (c) Neither the mother nor the father has influenza (d) All the family members have influenza

2. Consider a family with a mother, father, and two children. Consider the following set of events: A1={mother has influenza}; A2={father has influenza}; A3={first childhas influenza}; A4={second child has influenza}; B={at least one childhas influenza}; C={at least one parent has influenza}; D={at least one family memberhasinfluenza}. Are A3and A4mutually exclusive events? (a) Yes (b) No (c) Maybe

3. Consider a family with a mother, father, and two children. Consider the following set of events: A1={mother has influenza}; A2={father has influenza}; A3={first childhas influenza}; A4={second child has influenza}; B={at least one childhas influenza}; C={at least one parent has influenza}; D={at least one family memberhasinfluenza}. Express D in terms of B and C (a) D = B or C (b) D = B & C (c) D does not equal B or C

4. Consider a family with a mother, father, and two children. Consider the following set of events: A1={mother has influenza}; A2={father has influenza}; A3={first childhas influenza}; A4={second child has influenza}; B={at least one childhas influenza}; C={at least one parent has influenza}; D={at least one family memberhasinfluenza}.

Suppose an influenza epidemic strikes a city. In 10% of families, the mother has influenza. In 10% of families, the father has influenza. In 2% of families, both the mother and father have influenza. Furthermore, suppose each child has a 20% chance of contracting influenza and there is a 10% chance both children become diseased. What is the probability that at leastonechildwill get influenza? (a) 0.1 (b) 0.2 (c) 0.3 (d) 0.4