The packaging of an E.P.T. Pregnancy Test states that the test is "99\% accurate at detecting typical pregnancy hormone levels." Assume that the probability that the test will correctly identify a pregnancy is 0.99 and that 12 randomly selected pregnant women with typical hormone levels are each given the test. What is the probability that all 12 tests will be positive? In other words, what is the probability that all 12 tests correctly identify a pregnancy? Round to the nearest thousandth What is the probability that at least one test will not be positive? Round to the nearest thousandth

Step 1 ：The problem states that the accuracy of the E.P.T. Pregnancy Test is 99%, or 0.99. This means that the probability of the test correctly identifying a pregnancy is 0.99.

Step 2 ：We are asked to find the probability that all 12 tests will be positive. Since each test is independent of the others, we can simply multiply the probabilities together. So, the probability that all 12 tests are positive is \(0.99^{12}\).

Step 3 ：We are also asked to find the probability that at least one test will not be positive. This is the complement of the event that all tests are positive. So we can calculate this by subtracting the probability that all tests are positive from 1, which is \(1 - 0.99^{12}\).

Step 4 ：Using Python to calculate, we find that the probability that all 12 tests will be positive is approximately 0.886, and the probability that at least one test will not be positive is approximately 0.114.

Step 5 ：Final Answer: The probability that all 12 tests will be positive is \(\boxed{0.886}\). The probability that at least one test will not be positive is \(\boxed{0.114}\).