I have to solve this problem for a decision analysis network:
"There is a genetic trait present in 20% of the population that makes that, for men over 65 years, the probability of suffering the type of cancer mentioned in the previous exercise is 15%, while for those who do not have that trait the probability is 2.5%."
In the previous exercise says:
"The prevalence of a certain type of cancer among men over 65 years of age is 5%."
I have created a decision analysis network with two chance nodes: one from the genetic trait, and another one for the cancer. There is an connect from the genetic node to the cancer node.
I have calculated the probability for the genetic node (I called it G):
$$P(+g)=0.2$$ $$P(\neg g)=0.8$$
But I don't know how to calculate the probability for the cancer node (I called it X). I think its value depends on the genetic trait, so it is a conditional probability, but I don't know how that 5% in "The prevalence of a certain type of cancer among men over 65 years of age is 5%." is need it to compute the probability (or maybe I don't need to use it).
How can I compute the probability for node X?
If genetic trait is represented by G variable, and the probability of suffering a cancer is represented by X variable. I need to compute the following probabilities:
$$P(+x|+g)$$ $$P(+x|\neg g)$$ $$P(\neg x|+g)$$ $$P(\neg x|\neg g)$$