4. [14 pts] An emission test is being performed on :2 individual automobiles. Each car can be tested separately, but this is expensive. Pooling (grouping) can decrease the cost: The emission samples of k cars can be pooled and analyzed together. If the test on the pooled sample is negative, this 1 test sufces for the whole group of k cars and no more tests are needed for this group. If the test on the pooled sample is positive, then each of the k automobiles in this group must be tested separately. This strategy is referred to as a (n,k)- pooling strategy. Suppose that we create n/k disjoint groups of k automobiles (assume n is divisible by k) and use the pooling method. Assume the probability that a car tests positive is p, and that each of the n individuals autos are \"independent,\" i.e., their tests are independent of one another. Finally suppose that the cost for testing an emission sample is C, no matter how many individual elements are pooled in the sample. 4.1. [6 pts] Given a pooled sample of k autos, what is the expected cost to test the sample so that results are known for each individual auto? 4.2. [4 pts] Compute the testing cost per car for n = 1000, p = 0.02, k = 10, C = $100.00 4.3. [4 pts] Compute the testing cost per car for n = 1000, p = 0.02, k = 5, C = $100.00