i need help with 1-5

The Vermont Department of Health offers a service of testing water samples for the bacteria E. Coli. To save time and money, the state could test thase samples in batches. Suppose they batch them into groups of three. If the batch passes, then all three pass. If the batch fails, then each member is to be tested individually. Assume the department of health receives 300 samples and they subgroup these into 100 batches of 3 samples each. Further, assume there is a 5% chance of nding E. Coli in any single sample. Answer the following questions. 1. What is the probability that any batch of three samples will test positive for E. 0011. 2. Based on your previous answer, how many of the 100 groups of 3 do you expect will test positive? 3. Based on your previous answer, what is the expected number of tests that need to be run using this method? Is this better than testing all 300 samples individually? 4. Would the situation improve if you were to group them in batches of 5? 5. What is the optimal batch size for this particular