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Treatment for endocarditis is risky. The patient will (a) die in the hospital, (b) partially recover,...

Treatment for endocarditis is risky. The patient will (a) die in the hospital, (b) partially recover, or (c) fully recover. With full recovery, the patient can expect to live for another 20 years, but only 25 percent of patients fully recover. With partial recovery, the patient can expect to live 10 more years. However, 20 percent of patients die in the hospital. Assuming patients usually live just one year without treatment, what is the expected value of the treatment expressed as additional years of life?

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Answer #1

Probability to fully recovery = .25

Probability of die in the hospital = .20

Probability of partial recovery = 1 - .25 - .20 = .55

So,

expected value of treatment = .25*20 + .20*1 + .55*10

expected value of treatment =  10.7 years

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