Question
Betty has just returned home from a discussion with her mechanic about her Vintage Z3. Her mechanic tells her that he thinks the ignition coils
Betty has just returned home from a discussion with her mechanic about her Vintage Z3. Her mechanic tells her that he thinks the ignition coils (there are 4 of them) in her car are in poor shape and are going to fail and thus should be replaced. Furthermore, he tells her that on any given morning, there is a 6% chance that a specific coil will not work. He believes this is true for each of the four coils in the engine - they are all in poor shape. He also tells her that if one fails, the engine will likely run okay, but if there aren't at least 3 operating coils, the engine will not start. Assume coil failures are independent of each other. What is the probability that her car will start, based on the mechanic's information?
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