Thread: 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

Looks correct to me.