Soa #28

[newbie1]

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

[newbie1]

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