SOLUTION: You are seeking medical advice for an experimental treatment that may improve your life expectancy. The doctor informs you the probability of success after the treatment is 60% to

Question 884581: You are seeking medical advice for an experimental treatment that may improve your life expectancy. The doctor informs you the probability of success after the treatment is 60% to live 20 more years and the probability of failure is 40%. If it fails, you will die and if you do nothing you will live less than the 5 years. Based on the expected value of this situation, what would you decide? Do you agree with this decision or not? Why?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
tough call.
let's see what this means in money terms.
you can keep 5 dollars or you can bet it.
if you bet it, you will get back 20 dollars 60% of the time and you will get back nothing 40% of the time.

your expected value if you bet it is:
EV = .6 * 20 + .4 * 0 which is equal to 12 dollars.

your expected value if you don't bet is 5 dollars.

your net average gain per bet is 7 dollars.

what this means is if you bet 100 times, you would get back 20 dollars 60 of those times and you would get back nothing 40 of those times.

after 100 bets, you would have gotten back 1200 dollars because 60 * 20 = 1200.

divide that by the number of times that you bet, and it comes out to be an average of 12 dollars per bet because 1200 / 100 = 12.

so, based on expected value alone, you would want to bet the 5 dollars because you could expect an average of 12 dollars back on each bet which gives you a net gain of 5 dollars per bet.

only problem is, you're not betting 5 dollars.

you're betting 5 years of your life.

if you lost, you don't get to bet again.

that puts a whole new slant on it.

based on expected value of life expectancy only, you might still consider doing it, but so many other factors come into play, that the decision cannot possible rest on expected value alone.

one of the factors that might go into the decision is how important it is for you to live the next several years versus how important is it for you to live more than that.

another factor might be cost. if it costs a bundle and you and your family wind up broke regardless of whether you survive or not, you may have gained several years but you and your family's quality of life has deteriorated greatly. In fact, if you take the procedure and lose, your family is in the hole financially and they've lost you as well. that's not a very exciting possibility for them, and for you, if you care about what happens to them as well.

i would not agree with the decision based only on expected value of number of years left for you to live.
the basic assumption of expected value is meaningless when you're dealing with a bet of 5 years of your life instead of a bet of 5 dollars.
too many other factors come into play that can affect the decision as well.
you do not get to bet again if you lose.

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