Actuarial Outpost
 
Go Back   Actuarial Outpost > Exams - Please Limit Discussion to Exam-Related Topics > SoA/CAS Preliminary Exams > Probability
FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions

DW Simpson Global Actuarial & Analytics Recruitment
Download our Actuarial Salary Survey
now with state-by-state salary information!


Probability Old Exam P Forum

Reply
 
Thread Tools Search this Thread Display Modes
  #1  
Old 03-27-2020, 11:31 AM
jdzhou jdzhou is offline
SOA
 
Join Date: Oct 2019
College: University at Buffalo (Alumni)
Posts: 3
Unhappy 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?
Reply With Quote
  #2  
Old 03-27-2020, 11:42 AM
Vorian Atreides's Avatar
Vorian Atreides Vorian Atreides is offline
Wiki/Note Contributor
CAS
 
Join Date: Apr 2005
Location: As far as 3 cups of sugar will take you
Studying for CSPA
College: Hard Knocks
Favorite beer: Most German dark lagers
Posts: 68,187
Default

Approach the problem from the "complement" . . .

What's the probability of having exactly {0, 1, 2} faulty vials given that the batch is APPROVED?
__________________
I find your lack of faith disturbing

Why should I worry about dying? Itís not going to happen in my lifetime!


Freedom of speech is not a license to discourtesy

#BLACKMATTERLIVES
Reply With Quote
  #3  
Old 03-27-2020, 11:49 AM
Gandalf's Avatar
Gandalf Gandalf is offline
Site Supporter
Site Supporter
SOA
 
Join Date: Nov 2001
Location: Middle Earth
Posts: 31,529
Default

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.
Reply With Quote
  #4  
Old 03-27-2020, 12:47 PM
jdzhou jdzhou is offline
SOA
 
Join Date: Oct 2019
College: University at Buffalo (Alumni)
Posts: 3
Default

If this was sampling without replacement, could you define the number of defective vials as a hypergeometric random variable?
Reply With Quote
  #5  
Old 03-27-2020, 01:05 PM
jdzhou jdzhou is offline
SOA
 
Join Date: Oct 2019
College: University at Buffalo (Alumni)
Posts: 3
Default

Never mind, that's still useless in regards to solving the problem.
Reply With Quote
  #6  
Old 03-27-2020, 01:09 PM
Vorian Atreides's Avatar
Vorian Atreides Vorian Atreides is offline
Wiki/Note Contributor
CAS
 
Join Date: Apr 2005
Location: As far as 3 cups of sugar will take you
Studying for CSPA
College: Hard Knocks
Favorite beer: Most German dark lagers
Posts: 68,187
Default

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.
__________________
I find your lack of faith disturbing

Why should I worry about dying? Itís not going to happen in my lifetime!


Freedom of speech is not a license to discourtesy

#BLACKMATTERLIVES
Reply With Quote
Reply

Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off


All times are GMT -4. The time now is 10:21 PM.


Powered by vBulletin®
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.
*PLEASE NOTE: Posts are not checked for accuracy, and do not
represent the views of the Actuarial Outpost or its sponsors.
Page generated in 0.28293 seconds with 11 queries