What is the likelihood of being infected with covid-19 if I have 3 of the main symptoms? I'm trying to formulate this as a bayesian statistics problem, would appreciate any suggestions.
For example the symptoms can be fever, muscle ache, diarrhea. This table from a 2020 study shows the percentage of infected patients (total 99) that show a particular symptom
Fever (83%) Cough (82%) Shortness of breath (31%) Muscle ache (11%) Confusion (9%) Headache (8%) Sore throat (5%) Rhinorrhoea (4%) Chest pain (2%) Diarrhoea (2%) Nausea and vomiting (1%)
In other words given a probability $S_i$ for each symptom and showing k number of symptoms, what is the likelihood $P$ that I'm infected? Using $P(A|B) = P(B|A) \cdot P(A) / P(B)$, I think the main formulation is:
$$ P(c19 | [fever, cough, \cdots]) = P(c19 | S_1) \cdot P(c19 | S_2) \cdots P(c19 | S_k) / X $$ Here $X$ combines all $P(B)$ for each symptom, but what is P(B) for each symptom? and do the probabilities simply multiply?