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An elderly patient is a candidate for an experimental operation. The operation has a 70% chance of allowing her to live 8 more years on average; a 20% chance of having no effect and allowing her to live 4 more years on average; and a 10% chance of making the condition worse and allowing her to live 1 more year on average. What is the expected number of years the patient will live if she undergoes the operation?
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