I need help with the following question:
A study of the relationship between blood pressure and cholesterol level showed the following results for people who took part in the study:
(i) of those who had high blood pressure, 50% had a high cholesterol level, and
(ii) of those who had high cholesterol level, 80% had high blood pressure.
Of those in the study who had at least one of the conditions of high blood pressure or high cholesterol level, what is the proportion who had both conditions?
With only P(X|Y) = 0.8 and P(Y|X) = 0.5 given, how would I be able to derive P(X and Y) from the 2 conditional probability
I understand that P(X|Y) = P(X and Y)/P(X) and P(Y|X) = P(Y and X)/P(Y) but I'm not sure how to proceed on from here. I would be very grateful to receive any constructive feedback regarding my question. Thank you!
with Bayes' formula we have $$P(Y|X)=P(X|Y)\frac{P(Y)}{P(X)}$$ then $$P(X)=8/5P(Y)$$ but you cannot obtain any other information