Your doctor tells you that blood tests indicate that there i

Your doctor tells you that blood tests indicate that there is a 10% chance that you have a terrible disease which will shave 10 years off of your lifespan. There is a treatment for this disease, which completely cures it, but the treatment has a 1% chance of immediately killing you. If you expected to live for 60 more years before hearing this news, and if each year of future life is equally precious to you, should you take the treatment?

Solution

Let\'s calculate expected lifespan in both the scenario.

Expected Value = Probability of event * Value of the event

Case 1 : Not taking the treatment

Expected loss = 10% * 10 = 1 Year

Case 2 : Taking the treatment

Expected loss = 1% * 60 = 0.6 Years

So you should take the treatment as this has lower expected loss than the other.