2. [15 pts total] One percent of all individuals in a certain population are carriers of a particular disease. A diagnostic test for this disease has a 90% detection rate for carriers and a 5% detection rate for non-carriers. Suppose the test is applied independently to two different blood samples from the same randomly selected individual.

(a) [6 pts] Draw a probability tree that describes this experiment. Be sure to carefully define your notation and write the joint probabilities at the end of each branch.

(b) [6 pts] What is the probability that both tests yield the same result?

(c) [3 pts] If both tests are positive, what is the probability that the selected individual is a carrier?