Not to be too pedantic but your back of the envelope probabilities are based on inaccurate assumptions and probably several orders of magnitude off. Specifically, your not just assuming uniform but also independent from one day to the next. A more accurate treatment would be to assume conditional dependence from one day to the next (the Markov property). Once you have a record hot day, you are significantly more likely to have another record hot day following it.
That said, it’s still low probability, just not as low as what you’re saying.
Not to be too pedantic but your back of the envelope probabilities are based on inaccurate assumptions and probably several orders of magnitude off. Specifically, your not just assuming uniform but also independent from one day to the next. A more accurate treatment would be to assume conditional dependence from one day to the next (the Markov property). Once you have a record hot day, you are significantly more likely to have another record hot day following it.
That said, it’s still low probability, just not as low as what you’re saying.
Any thoughts on how I could incorporate that for a better back of the napkin?
(Also, that number is only consider that the number presented was based on 7 independent events, not 34)