Exercise 1. Conditional Probability. Suppose that 5% of the employees of a certain company use illegal drugs. The company performs random drug tests that return positive results 98% of the time if the person is a drug user. However, it also has a 4% false positive rate. The results of the test are independent from test to test for a given person. Round your answers to 4 decimals points. Reminder: The false positive rate of a test is defined as the probability that the test returns a positive result while the person was not taking drugs. 1. An employee at the company has a positive test. What is the probability that he uses drugs? 2. Knowing that the first test was positive, what is the probability the second test will be positive? 3. Suppose that the second test is also positive. What is the probability he uses drugs?

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.