Finding the Probability

Question

A hospital receives 20% of its COVID-19 vaccine shipments from Canada and the remainder of its shipments from neighbouring countries. Each shipment contains a very large number of vaccine vials. For Canada’s shipments, 10% of the vials are ineffective. For the neighbouring countries, 2% of the vials are ineffective. The hospital tests 30 randomly selected vials from a shipment and finds that one is ineffective. What is the probability that the shipment came from Canada.

Answer 1

Hi Junior S., the probability is 0%. Of current COVID-19 vaccine clinical trial originators, 4 are in USA, 1 in UK, and 4 in China. Thus, none would come from Canada. Unless you (and the President) know something the rest of the world (ROW) doesn't.

However, if you take this as a pure math thing, convert the two sources into probabilities for 1 / 30 fails (using binomial probability calculators), then use equalization for the sourcing. So for Canada, P(1/30) = 0.14130386092; for

Neighbors P(1/30) = 0.33396999146. Note that this is larger, b/c Canada-sourced has mostly >1/30 fails.

After equalization for the sourcing (multiply by the fraction sourced) values are 0.02826077218 and 0.26717599316 respectively. Normalize these two values from 0.29543676534 total to 1 total, P respectively is

0.09565760086 and 0.90434239913 .

So the probability that the shipment came from Canada is 0.096, and the probability that this hospital will be shut down soon b/c it keeps losing paperwork (evidently, or why calculate this?) approaches 1.0 . Just sayin'.

-- Cheers, -- Mr. d.