please show the work.

Flag question: Question 5 Question 51 pts Consider the context presented in your textbook: "A patient named Fred is tested for a disease called conditionitis, a medical condition that afflicts 1% of the population. The test result is positive, i.e., the test claims that Fred has the disease. Let D be the event that Fred has the disease and T be the event that he tests positive. Suppose that the test is "95% accurate"; there are different measures of the accuracy of a test, but in this problem it is assumed to mean that P(TID) = 0.95 and P(Tc|Dc) = 0.95. The quantity P(TID) is known as the sensitivity or true positive rate of the test, and P(Tc|Dc) is known as the specificity or true negative rate." Fred tests positive and, knowing that the probability of actually having the disease is only 16%, decides to take a second test. He tests positive a second time. He does the math presented in the example of your textbook and, realizing that the probability that he actually has the disease is still "only" 78%. Therefore, he decides to take a third test and, again, tests positive. What is the probability, in percentage, that he actually has the disease, given that he tested positive three times, in three independent tests (all with the same 95% accuracy)? Round your result to the nearest integer (For instance, enter 2% if you get a probability of 0.023, or 3% if you get a probability of 0.025). Answer: %