The following problem is under the Bernoulli chapter in my book and it's about conditional convergence.
A hospital obtains its flu vaccines:
40% from A
50% from B
10% from C
Amount of ineffective vaccines:
3% in A
2% in B
5% in C
The hospital tests 5 vials from each shipment. If at least one of the five is ineffective, find the conditional probability of that shipment's having come from C.
I know how to solve the problem if the information in bold was not given. But I don't know how the information in bold changes the problem. Can any one explain ? How do I factor in them testing 5 vials.
We know that 5% of the vials from C are defected.
We know that 10% of all vials come from C
The test fails if at least on vial is defected: .
In other words, not all five pass.
But again what about P(F|C) is 0.03?