B let b be the event you get a 3 on your first roll

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b) Let B be the event you get a 3 on your first roll . Find 𝑃(? ∪ ?) . c) Are events A and B independent? Justify your answer. 12. Three machines A, B, and C are used to produce a large quantity of identical parts at a factory. Machine A produces 60% of the parts, while Machine B and C produce 30% and 10% of the parts, respectively. Historical records indicate that 10% of the parts produced by Machine A are defective, compared with 30% for Machine B and 40% for Machine C. a) Draw a tree diagram to represent this chance process. b) If we choose a part produced by one of these three machines, what s the probability that it s defective? Show your work. c) If a part is inspected and found to be defective, which machine is most likely to have produced it?
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13. Based on previous records, 17% of the vehicles passing through a tollbooth have out-of-state plates. A bored tollbooth worker decides to pass the time by counting how many vehicles pass through until he sees two with out-of-state plates. a) Describe the design of a simulation to estimate the average number of vehicles it takes to find two with out-of-state plates. Explain clearly how you will use the partial table of random digits below to carry out your simulation. b) Perform five repetitions of the simulation you described in part (a) using the table below. Be sure to give the results of each trial and give your estimate for the number of cars expected. 41050 92031 06449 05059 59884 31880 53115 84469 94868 57967 05811 84514 84177 06757 17613 15582 51506 81435 75011 13006 63395 55041 15866 06589
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