6.0 It is common in many industrial areas to use a filling machine to fill boxes full of product. This occurs in the food industry as well as other areas in which the product is used in the home, for example, detergent. These machines are not perfect, and indeed they may A, fill to specification, B, underfill, and C, overfill. Generally, the practice of underfilling is that which one hopes to avoid. Let P(B) - 0.003 while P (A) = 0.970. (a) Give P(C). (b) What is the probability that the machine does not underfill? (c) What is the probability that the machine either overfills or underfills? 7.0 Consider the situation of the previous question: Suppose 70,000 boxes of detergent are produced per week and suppose also that those underfilled are "sent back," with customers requesting reimbursement of the purchase price. Suppose also that the cost of production is known to be $4.00 per box while the purchase price is $4.50 per box. (a) What is the weekly profit under the condition of no defective boxes? (b) What is the loss in profit expected due to under- filling? 8.0 A class in advanced physics is composed of 45 juniors, 84 seniors, and 20 graduate students. The final grades show that 13 of the juniors, 25 of the seniors, and 18 of the graduate students received an A for the course. If a student is chosen at random from this class and is found to have earned an A, what is the probability that he or she is a senior? 9.0 There is money to send two of eight city council members to a conference in Honolulu. All want to go, so they decide to choose the members to go to the conference by a random process. How many different combinations of two council members can be selected from the eight who want to go to the conference