b) If none of the last ten customers has ordered the pork entrée, consider how many additional customers will place order until there are three more orders for the pork entrée. Find its distribution, expected value, and variance. c) What is the probability that the next ten orders will include three chicken entrées, four beef entrées, and three pork entrées? d) If the next forty orders include exactly sixteen chicken entrées, consider how many of the first ten of those orders are for the chicken entrée. Find its distribution, expected value, and variance. In parts (d) and (e), consider a different situation, where we are testing for a disease D that we think is present, D+, with probability 0.4, and absent, D−, with probability 0.6. We believe that a test has sensitivity P{T+∣D+}=0.75 and specificity P{T−∣D−}=0.8. e) What is our probability that the disease is present if we perform the test and it is positive, T+. and our probability the disease is absent if that test is negative, T− ? f) Suppose we perform three tests, conditionally independent given D. Given each possible number of positive test results, 0,1,2, or 3 , what is our probability that the disease is present?