D.W. Simpson Worldwide Actuarial Recruitment Life Health Pension Casualty US Asia Australia Europe Salary Apply Ezra Penland Actuarial Recruiters Top Actuary Jobs Salary Surveys Apply Bios Casualty Health Life Pension Pauline Reimer, ASA, MAAA Pryor AssociatesActuarial Openings: Life, P&C, Health, Pensions, Finance Advertise Here Contact us at actuary@actuary.com or 770-425-8576Reach top actuarial professionals

1. ## 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. 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

There are currently 1 users browsing this thread. (0 members and 1 guests)

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•