14. Directions: Show all your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy of your results and explanation. Two antibiotics are available as treatment for a common ear infection in children. . Antibiotic A is known to effectively cure the infection 60 percent of the time. Treatment with antibiotic A costs $50. - Antibiotic B is known to effectively cure the infection 90 percent of the time. Treatment with antibiotic B costs $80. The antibiotics work independently of one another. Both antibiotics can be safely administered to children. A health insurance company intends to recommend one of the following two plans of treatment for children with this ear infection. - Plan I: Treat with antibiotic A first. If it is not effective, then treat with antibiotic B. 0 Plan 11: Treat with antibiotic B rst. If it is not effective, then treat with antibiotic A. a. If a doctor treats a child with an ear infection using plan I, what is the probability that the child will be cured? If a doctor treats a child with an ear infection using plan 11, what is the probability that the child will be cured? b. Compute the expected cost per child when plan I is used for treatment. Compute the expected cost per child when plan 11 is used for treatment. e. Based on the results in parts (a) and (b), which plan would you recommend? Explain your recommendation