Unbelievable Things
Post #693
One of the lowest probabilities on a topic of interest is the probability of winning the jackpot in the Mega Millions lottery: Just 3.3 chances in a billion. You apparently pick the first 5 balls using numbers from 1 to 70, forming 12,103,014 possible combinations, one of them being a winner. Then you pick a 6th ball from 1 to 25.
A comparable probability is when there is a process with an expected number of instances or occurrences of “20” and you end up getting “zero.” In 40 coin flips, there is a long-run expectation of 20 heads. If you flip a coin 40 times, getting tails every time (no heads), the chances are lower than they are to win Mega Millions.
Back in April of 2020, the WHO compiled reports about the deaths aboard the Diamond Princess cruise ship. The report on April Fool’s Day was believable, where they reported 7 total deaths. It was 46 days past the last passenger infection found. But then they eventually added 6 more deaths by 18 Apr 2020:
But, because 98.6% of COVID deaths occur within 46 days of symptom onset, the chance to see 6 of 13 deaths occur when probability on those last 6 is that tiny remainder of all probability — (100% - 98.6%) = 1.4% = 0.014 — is only 1 chance in 84 million (12 chances in a billion), and that doesn’t account for dwindling of probability.
You are more likely to win Mega Millions than for the WHO to have been honest when they put together that Situation Report #89 on 18 Apr 2020.
Reference
[“Time-to-death” probability for COVID. Upper bound of confidence interval around mean and SD indicate 98.6% of all COVID deaths will have occurred by Day 46] — Linton NM, Kobayashi T, Yang Y, et al. Incubation Period and Other Epidemiological Characteristics of 2019 Novel Coronavirus Infections with Right Truncation: A Statistical Analysis of Publicly Available Case Data. Journal of Clinical Medicine. 2020 Feb;9(2). DOI: 10.3390/jcm9020538. PMID: 32079150; PMCID: PMC7074197. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7074197/
[WHO COVID-19 Situation Report #72 on 1 Apr 2020 showing 7 Diamond Princess deaths (46 days after all passenger infections had occurred)] — WHO. https://www.who.int/docs/default-source/coronaviruse/situation-reports/20200401-sitrep-72-covid-19.pdf
[WHO COVID-19 Situation Report #89 on 18 Apr 2020 showing 13 Diamond Princess deaths (63 days after all passenger infections had occurred)] — WHO. https://www.who.int/docs/default-source/coronaviruse/situation-reports/20200418-sitrep-89-covid-19.pdf