Reference no: EM132851811

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 child has influenza}

A4 = {second child has influenza}

B = {at least one child has influenza}

C = {at least one parent has influenza}

D = {at least one family member has influenza}.

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.

a.Considering the set of events A1 and A2 independent?

b. What is the probability that at least one child will get influenza?

c. Based on your result from Part (a), what is the conditional probability that the father has influenza given the mother has influenza?