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
Actuarial Jobs

Visit our site for the most up to date jobs for actuaries.

Actuarial Salary Surveys
Property & Casualty, Health, Life, Pension and Non-Tradtional Jobs.

Actuarial Meeting Schedule
Browse this year's meetings and which recruiters will attend.

Contact DW Simpson
Have a question?
Let's talk.
You'll be glad you did.


Probability Old Exam P Forum

Reply
 
Thread Tools Search this Thread Display Modes
  #1  
Old 04-04-2020, 08:16 PM
jenben jenben is offline
CAS SOA CCA
 
Join Date: May 2019
College: Alumni
Posts: 22
Default Multiplication Theorem of Probability

A psychology experiment on memory was conducted which required participants to note which songs they found pleasing. Based on many results, the (partial) probability distribution below was determined for the discrete random variable X = number of songs found pleasing (during a fixed time period).

X = # songs 1 2 3 4 5 6 7 8 9 10
Probability 0 0.02 0.04 0.07 0.15 0.18 0.24 0.14 0.11 0.05


Given that the person finds at least 7 songs pleasing to the ear, what is the probability that they find 8 songs pleasing to the ear? Please round to the second decimal point.

Should it be = 0.14/(0.24+0.14+0.11+0.05)
or
= 0.14/(0.24+0.14)
Reply With Quote
  #2  
Old 04-04-2020, 08:41 PM
Gandalf's Avatar
Gandalf Gandalf is offline
Site Supporter
Site Supporter
SOA
 
Join Date: Nov 2001
Location: Middle Earth
Posts: 31,581
Default

should be (.14+.11+.05)/(.24+.14+.11+.05) if I understand the question and givens
Reply With Quote
  #3  
Old 04-04-2020, 08:53 PM
jenben jenben is offline
CAS SOA CCA
 
Join Date: May 2019
College: Alumni
Posts: 22
Default

Thanks for the response but this is where I have a confusion. Do we need to check about (.11+.05), when in the question they ask about only 8 ?
Reply With Quote
  #4  
Old 04-04-2020, 09:17 PM
Gandalf's Avatar
Gandalf Gandalf is offline
Site Supporter
Site Supporter
SOA
 
Join Date: Nov 2001
Location: Middle Earth
Posts: 31,581
Default

Question is not stated precisely. I gave the answer for "at least 8". If the question intends "exactly 8" the numerator would be different.
Reply With Quote
  #5  
Old 04-04-2020, 09:26 PM
jenben jenben is offline
CAS SOA CCA
 
Join Date: May 2019
College: Alumni
Posts: 22
Default

Is there any rule if neither "at least" nor "exactly" is given ? Like in this example, it's given that what is the probability that they find 8 songs pleasing to the ear?
Reply With Quote
  #6  
Old 04-04-2020, 09:35 PM
Gandalf's Avatar
Gandalf Gandalf is offline
Site Supporter
Site Supporter
SOA
 
Join Date: Nov 2001
Location: Middle Earth
Posts: 31,581
Default

For an actual exam question, there would have been many reviewers discussing the wording, so it would likely be precise. Exam P and most of the prelims have pilot questions that don't count, where imprecise wording might inadvertently slip through many reviewers. If it is a real question on P, then it has been given before, and I hope they would have seen an unexpected cluster of wrong answers that would tell them to rethink the wording. But I don't know the actual process, and defective questions could still get through.
Reply With Quote
  #7  
Old 04-04-2020, 09:38 PM
Gandalf's Avatar
Gandalf Gandalf is offline
Site Supporter
Site Supporter
SOA
 
Join Date: Nov 2001
Location: Middle Earth
Posts: 31,581
Default

Where did you get the problem, and did it have an answer with it? Then, after the fact, you can see whether the author intended to mean exactly 8 or at least 8. Maybe the best interpretation of the wording is exactly 8.
Reply With Quote
  #8  
Old 04-04-2020, 09:51 PM
jenben jenben is offline
CAS SOA CCA
 
Join Date: May 2019
College: Alumni
Posts: 22
Default

In my company, they have sample question. This one I just couldn't figure out. I think you are right the wording means is exactly 8. I will ask my office guys what's the right answer?
Reply With Quote
  #9  
Old 04-04-2020, 10:06 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: 68,553
Default

IMO, as worded, I would interpret it as "(exactly) eight". If the intent would be to answer "either 8 or 9 or . . .", then the wording would be required to indicate it as such.


With that said, as Gandalf points out, there are cases of typos and forgotten wording, but I would expect that (exactly) eight should be the correct answer given the wording, regardless of intent.
__________________
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 06:15 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 0.45999 seconds with 11 queries