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Question Details:
About two years ago, your narrator entered a Starbucks near his home1.
When the individual in front of him came to the head of the line, a cup of “half-caf” was
ordered, with a request to “put the decaf in first”. When the Barista placed the coffee on the
counter, she was queried as to whether she had, indeed, put the decaf in first. She thought
for a moment, and said “Actually, I didn’t.” The customer then spoke up, speaking of being
very tired and of a desire for the first sip to have a big jolt. Another cup of coffee was then
requested, a “half-caf” prepared according to specifications. The Barista then said “You
know, it doesn’t matter”, but the customer countered with “If you put the decaf in first,
the strong stuff will be at the top, and that is what I want”, to which the Barista shot your
narrator a look and complied with customer demands.
Given that ergodic behavior of the caffeine molecules was probably established a few
milliseconds after preparation, calculate the probability (using a reasonable estimate of the
number of caffeine molecules in a 12 oz. cup of coffee) that more than 50.00000001% of
the molecules would be in the upper 6 oz of a cup of coffee prepared by the customer’s
specifications.
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