Question

A hospital receives 30% of its COVID-19 vaccine shipments from Ghana Health Service
and the remainder of its shipments from neighbouring West African countries. Each
shipment contains a very large number of vaccine vials. For GHS’s shipments, 8% of the
vials are ineffective and for the neighbouring countries, 3% 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 neighbouring West
African countries?

Answer 1

W = shipment from West Africa,

I = one vial is ineffective,

G = shipment from Ghana.

P(W)=1-0.3=0.7,

P(I|W)=$\begin{pmatrix} 30 \\ 1\end{pmatrix}$*0.03*0.97²⁹=0.372,

P(I|G)=$\begin{pmatrix} 30 \\ 1\end{pmatrix}$ *0.08*0.92²⁹=0.2138,

(P(I|W)*P(W))/(P(I|W)*P(W)+P(I|G)*P(G))=(0.372*0.7)/(0.372*0.7+0.2138*0.3)=0.8.