A doctor is trying to decide if a patient has one of three diseases d1, d2, or d3. Two tests are to be carried out, each of which results in a positive (P) or a negative (N) outcome. There are four possible test patterns PP, PN, NP, and NN. National records have indicated that, for 10,000 people having one of these three diseases, the distribution of diseases, and test results are as shown below: Please find the image below   What is the probability that a randomly selected patient has the 2nd disease d2? What is the probability that a randomly selected patient has a test result of NP? If a randomly selected patient gets a test result of NP, what is the probability that the patient has the third disease d3?

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