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Math Help - double probabilities and expected costs

  1. #1
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    double probabilities and expected costs

    I'm not really sure if i did this right... what i have so far is in blue... any help would be GREATLY appreciated!


    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.
    •Plan II: Treat with antibiotic B first. 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?
    0.60+ [(0.90)(0.40)]= 0.96

    If a doctor treats a child with an ear infection using plan II, what is the probability that the child will be cured?
    0.90+ [(0.60)(0.10)]= 0.96


    (b) Compute the expected cost per child when plan I is used for treatment.
    0.60($50)+ 0.40($130)= $82

    Compute the expected cost per child when plan II is used for treatment.
    0.90($80)+ 0.10($130)= $85
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  2. #2
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    Looks correct to me.
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