Trump is diagnosed with an uncommon disease. He knows that there is only a 1% chance of getting it. Use the letter D for the event "he has the disease" and T for "the test says so". It is known that the test is imperfect:(|)=0.98 and(|)=0.95.

1. a) What is the false-positive rate?

1. b) What is the false-negative rate?
3. c) Given that he tests positive, what is the probability that he really has the disease?

1. d) He obtains a second opinion: an independent repetition of the test. He tests positive again. Given this, what is the probability that he really has the disease?