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

P(1 is ineffective)=P(From GHS)*P(1 is ineffective|From GHS)+P(From neighbouring countries )*P(1 is ineffective|From neighbouring countries )

=0.3*(30C1)*(0.08)¹(0.92)²⁹+0.7*(30C1)*(0.03)¹(0.97)²⁹

=0.3*0.213825+0.7*0.372068

=0.324595

therefore

P(From neighbouring countries |1 is ineffective)

=P(From neighbouring countries )*P(1 is ineffective|From neighbouring countries)/P(1 is ineffective)

=0.7*(30C1)*(0.03)¹(0.97)²⁹/0.324595

=0.7*0.372068/0.324595

=0.8024