Calculate the probability that 1 person (or more) is infected in group of size n

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1	Calculate the Probability that 1 Person (or more) is Infected in Group of Size n
2	Created by:	Dr. Jeff Gilchrist
3	Last updated:	January 3, 2022
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5	For more details on these calculations please see:	https://www.facebook.com/jeff.gilchrist.ca/posts/10157316541495766
6	For an index of my COVID-19 related articles see:	https://www.facebook.com/jeff.gilchrist.ca/posts/10156941150785766
7	Read this article for the background on the math:	https://blogs.scientificamerican.com/observations/online-covid-19-dashboard-calculates-how-risky-reopenings-and-gatherings-can-be/
8	Inspired by Ryan Imgrund's probabilty reports:	https://twitter.com/imgrund
9	For more daily COVID-19 related statistics and graphs:	http://gilchrist.ca/jeff/COVID-19/		http://gilchrist.ca/jeff/COVID-19/vaccine.html	http://gilchrist.ca/jeff/COVID-19/Ottawa.html
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11	Formula:		Where p is the per-person probability of being infected, and n is the size of the group
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13	Ottawa, ON, Canada
14	# Active COVID-19 Cases (Ottawa):	8952	Get latest from:	https://www.ottawapublichealth.ca/en/reports-research-and-statistics/daily-covid19-dashboard.aspx
15	Population (Ottawa):	1006210	See:	https://ottawa.ca/en/city-hall/get-know-your-city/statistics-and-economic-profile/statistics/current-population-and-household-estimates
16	Population (Ontario):	14745040	Q2 2020 See:	https://www150.statcan.gc.ca/t1/tbl1/en/tv.action?pid=1710000901
17	Seroprevalence (Ontario):	1.2%	October 31, 2020 data:	https://www.publichealthontario.ca/en/data-and-analysis/infectious-disease/covid-19-data-surveillance/covid-19-serosurveillance
18	Ottawa Cases on October 31, 2020:	7000	See:	https://open.ottawa.ca/datasets/covid-19-cases-and-deaths-in-ottawa
19	Ontario Cases on October 31, 2020:	75730	See:	https://data.ontario.ca/dataset/status-of-covid-19-cases-in-ontario
20	Seroprevalence Factor (Ontario):	2.33646480919
21	Per-person probability (p):	0.00889675118		Lower Bound: only known active cases from positive tests, best case scenario, doesn't account for those infected who never got tested
22	Seroprevalence (Ontario factor) per-person prob. (p):	0.02078694604		Seroprevalence (Ontario factor): active cases + factor for 1.2% prevalence of COVID-19 in Ontario via antibody blood tests, best estimate for real # of infections in a city
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24	Group Size (n)	Lower Bound (Active Cases)	Active + Seroprevalence (1.2%)
25	10	8.5%	18.9%
26	15	12.5%	27.0%
27	25	20.0%	40.9%
28	50	36.0%	65.0%
29	100	59.1%	87.8%
30	250	89.3%	99.5%
31	500	98.9%	100.0%
32	1000	100.0%	100.0%
33	2000	100.0%	100.0%
34	5000	100.0%	100.0%
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36	Note: Feel free to make a copy of this spreadsheet and change the # active cases, population, seroprevalence, and group sizes for your area and calculate what you are interested in knowing.
37	You can do this by selecting "File -> Make a copy" within Google Sheets which will let you edit the values.
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