If someone tossed 100 coins once every second, according to the source, about how often would they expect to land on the most orderly outcome, either all 100 heads or all 100 tails?
AOnce every 100 years
BOnce every 10^13 years
COnce every 2 x 10^22 years
DOnce every 1.27 x 10^30 years
Answer & Solution
Correct answer: C. Once every 2 x 10^22 years
1. Getting 100 heads or 100 tails requires landing on one of only 2 microstates out of the 1.27 x 10^30 total possible microstates for 100 coins.
2. Tossing once per second and needing such an enormously rare outcome means an enormously long expected wait.
3. This wait time is given directly: tossing the coins once each second, you could expect to get either 100 heads or 100 tails once in 2 x 10^22 years.
4. It adds that this period is 1 trillion times longer than the age of the universe, underscoring just how large the number is.
5. Option D uses the total microstate count itself as if it were a number of years, which is not the figure given for this waiting time.
6. Options A and B are both far too short to match the source's own stated figure of 2 x 10^22 years.
_Source: OpenStax College Physics (CC BY 4.0), Ch 15 "Thermodynamics", section 15.7 Statistical Interpretation of Entropy and the Second Law of Thermodynamics: The Underlying Explanation_
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