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Mathematics
Set Theory, Logic, Probability, Statistics
Troubleshooting Xmas Lights: Comparing Plan A & Plan B
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[QUOTE="nbalderaz, post: 338824, member: 17745"] In ancient times (the Twentieth Century) strings of Christmas lights were wired strictly in series, so if one bulb failed, the entire string would go dark. Consider two competing troubleshooting strategies: Plan A: You start at one end of the string and test each bulb in sequence, until you find the bad one, then replace it. Plan B: Using your trusty multimeter, you can test intervals of the string. You use it to perform a binary search for the bad bulb. Assume that every light in a string is equally likely to fail. (1) For a string of n lights, what is the probability that Plan A requires fewer tests than Plan B? (2) Calculate this probability for n = {16, 24}. [/QUOTE]
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Troubleshooting Xmas Lights: Comparing Plan A & Plan B
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