A doctor thinks, before testing, that the probability that his patient has XYZ disease is 85%.

He tests 5 times and gets 3 positive tests and 2 negatives.

When a patient does have XYZ, they test positive 70% of the time. Patients who do not have XYZ test positive 10% of the time.

Using conditional probability, what is the probability that the patient has XYZ?

So far I used table to find that the probabilities of the patient testing positive given they have XYZ is 87.5% and the probability of testing negative given the patient ahs XYZ is 12.5%

Am I in the right direction? Or did I miss something completely. How do I combine the probabilities of these individual tests to account for the probability that the patient has XYZ?