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#1




Difficult Question
Stumped by this question. Does this question make use of independence or some familiar distribution or even Bayes Theorem? Can you even calculate it without being given any values for probability? Here it is:
A pharmaceutical company is getting ready to deliver 100 vials of a flu vaccine. Before delivering those 100 vials, they randomly select 10 vials into the lab for quality testing. If any one of the vials fail the test, the delivery is cancelled. What is the probability that there are 3 or more faulty vials in an APPROVED batch? 
#2




Approach the problem from the "complement" . . .
What's the probability of having exactly {0, 1, 2} faulty vials given that the batch is APPROVED?
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#3




It does seem impossible without any further information. E.g., it's at least possible the answer could be 0, if you had been given that the 100 vials included no defective ones, or even that the 100 vials included at most 2 defective ones. Or answer 1, if you had been given that the 100 vials included at least 93 defective ones.

#6




The starting point needs to be some information about the (unconditional) probability that a vial is faulty.
I wonder if there is more to the problem that is described in the prior one or at the beginning of the section. Or that the problem is getting at the idea of recognizing the type of distribution is being described (so you'll need to "define" what the parameters are and then work out an symbolic (algebraic) solution rather than a numeric one). But you might consider starting with a "made up" value for the (unconditional) probability that a given vial is faulty and then see what you come up with for answer. Then you test distribution selections to see if you get a similar answer. For illustration, assume that the probability that a faulty vial makes it into the shipment is 2%. That is, if you randomly select one vial, there is a 2% probability that it is faulty.
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