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Thread: Soa #28

  1. #1
    Actuary.com - Level I Poster
    Join Date
    Aug 2013
    Posts
    23

    Soa #28

    Please break the solution into more steps to help me understand.

    A hospital receives 1/5 of its flu vaccine shipments from Company X and the remainder
    of its shipments from other companies. Each shipment contains a very large number of
    vaccine vials.
    For Company X’s shipments, 10% of the vials are ineffective. For every other company,
    2% of the vials are ineffective. The hospital tests 30 randomly selected vials from a
    shipment and finds that one vial is ineffective.
    What is the probability that this shipment came from Company X?
    (A) 0.10
    (B) 0.14
    (C) 0.37
    (D) 0.63
    (E) 0.86

    Solution: A
    Let
    C = Event that shipment came from Company X
    I1 = Event that one of the vaccine vials tested is ineffective
    Then by Bayes’ Formula,
    
    
    

    
    
    1
    1
    1 1
    |
    |
    | | c c
    P I C P C
    P C I
    P I C P C P I C P C
    
     
     

    Now

    

    

        
       
    30 29
    1 1
    30 29
    1 1
    1
    5
    1 1 1 4
    5 5
    | 0.10 0.90 0.141
    | 0.02 0.98 0.334
    c
    c
    P C
    P C P C
    P I C
    P I C
    
     
        
     
     
     
    Therefore,

       
    1      
    0.141 1/ 5
    | 0.096

  2. #2
    Actuary.com - Level I Poster
    Join Date
    Aug 2013
    Posts
    23
    Here are the links to the sample questions below:
    http://www.soa.org/Files/Edu/edu-exam-p-sample-quest.pdf
    http://www.soa.org/Files/Edu/edu-exam-p-sample-sol.pdf

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