Another group of researchers developed a new blood test to identify the same disease. The test result is given by a random variable X, with sensitivity and specificity given by 0.8 and 0.9, respectively (that means p(X = 1|D = 1) = 0.8 and p(X = 0|D = 0) = 0.9). If a patient did the blood test and the result is positive, what is the probability that the person has the disease?

Hint: you might want to use the Bayes Rule: p(b|a) = p(a|b)p(b) p(a)