Decision Tree


TS Contributor
A friend of mine asked me to help him with a decision tree .
I found an online calculator and some resource material but I am not sure how to plug in all the info.
Question is

Your patient may have a dangerous disease named Acute-Turkey-Overload(ATO). If not treated, Acute-Turkey-Overload (ATO) is fatal in 20% of cases. An operation, which is fatal in 10% of patients, always cures Acute-Turkey-Overload (ATO). The Shindig test is always positive in patients with Acute-Turkey-Overload(ATO). However the test is sometimes positive in patients who do not have Acute-Turkey-Overload (false positive).
Suppose you have done the Shindig test and it is positive. You look up the performance characteristics of the Shindig Test to decide whether to operate or not based on this result. At what probability of Acute-Turkey-Overload in a patient with a positive Shindig test would you be indifferent between operating and not operating ?
He even gave me his work so far which is
Let normal life expectancy have value = 1
And death have a value = 0

Die of surgery 0

Survive surgery 1.0
p[survival]=0.9 Die of ATO
ATO + p[die]=0.2

p[ATO] = Y


No surgery


p[no ATO]=1-Y

Now calculate the expected value of surgery, and the expected
Value of no surgery. These values should be equal. Solve for Y.
the calculator I found is
If you have any resource material regarding the question above please share.