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11 Data shows that approximately 3% of people have a specific disease. There is a test for this disease, but the result is not always accurate. If a sick person takes the test, there is 98% chance that the result of the test wil be positive. However, if a healthy person takes the test, there is 97% chance that the result of the test will be negative. If a random person from the population takes the test, (a) What is the probability that the result will be negative? Round the answer to 5 decimal places (b) State which theorems and/or definitions apply to the problem in part (a) (c) Given the result is negative, what is the probability that the person who took the test is actually sick? Round the answer to 5 decimal places. 12. One division of an Amazon fulillment center employs 3 people, U, V, and W, who pull items from shelves and assemble them for subsequent verification and packaging. U makes a mistake in an order five times in a hundred, and W makes a mistake in an order three times in a hundred (a) If U, V, and W fill, respectively, 30, 40, and 30 percent of all orders, what is the probability an order (gets a wrong item or the wrong quantity) one time in a hundred, V makes a mistake that if a mistake is made in an order, the order was filled by U? Round the answer to 5 decimal places. (b) State which theorems and/or definitions apply to the problem in part (a)

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