Christmas light

  • Thread starter nbalderaz
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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}.
 

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