of the individuals in this age group suffer from this fom o arthritis. The proposed test was given to individuals with confirmed arthritic disease, and a correct test result was obtained in 85% of the cases. When the test was administered to individuals of the same age group who were known onto be free of the disease, 4% were reported to have the disease. What is tne probability that an individual has this disease given that the test indicates its presence? 36. It is reported that 50% of all computer chips produced are defective. Inspec- tion ensures that only 5% of the chips legally marketed are defective. Unfor- tunately, some chips are stolen before inspection. If 1% of all chips on the market are stolen, find the probability that a given chip is stolen given that it is defective. 37. As society becomes dependent on computers, data must be communicated via public communication networks such as satellites, microwave systems, and telephones. When a message is received, it must be authenticated. This is done by using a secret enciphering key. Even though the key is secret, there is al- ways the possibility that it will fall into the wrong hands, thus allowing an ul old loinu f 19 NJA bist unggiavilidedorg.odt unauthentic message sages received are authentic. Furthermore, assume that only .1% thentic messages are sent using the correct key and that all authentic messages are sent using the correct key. Find the probability that a given that the correct key is used. Dov 1ed dong o bs0 to appear to be authentic. Assume that 95% of all mes- oidw.nove. of all unau- messäge is authentic REVIEW EXERCISES 38. A of engineering firms reveals that 80% have their own mainframe survey computer (M), 10% anticipate purchasing a mainframe computer in the near future (B), and 5% have a mainframe computer and anticipate buying another in the near future. Find the probability that a randomly selected firm: (a) has a mainframe computer or anticipates purchasing one in the near future (b) does not have a mainframe computer and does not anticipate purchasing lint one in the near future obr(c) anticipates purchasing a mainframe computer given that it does not cur- r d rently have one (d) has a mainframe computer given that it anticipates purchasing one in the me near future 39. In a' simulation program, three random two-digit numbers will be generated independently of one another. These numbers assume the values 00, 01, 02, ..., 99 with equal probability. (a) What is the probability that a given number will be less than 50? idadeng