can you explain what you did

3. Batch testing, or pooled testing, for COVID-19 was discussed early in the pandemic as a way to speed up the testing process and save testing supplies. An NPR article from July 6, 2020 discusses the process. Suppose that 12 people need to be tested for COVID-19. Assume that each person has a 10% chance of having the disease, independently from person to person. Consider two different plans for conducting the tests: . Plan A: Give an individual COVID test to each person. . Plan B: Combine samples from all 12 people into one batch and test that batch. . If at least one person has the disease, then the batch test result will be positive, and then all 12 people will need to be tested individually. . If nobody has the disease, then the batch test result will be negative, and no additional tests will be needed. Let the random variable X represent the total number of tests needed with Plan B (batch testing). a. Determine the probability distribution of X. (3 points)