Actuarial Outpost Optimal strategy for complicated true/false questions
 Register Blogs Wiki FAQ Calendar Search Today's Posts Mark Forums Read
 FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions

 Salary Surveys Property & Casualty, Life, Health & Pension Health Actuary JobsInsurance & Consulting jobs for Students, Associates & Fellows Actuarial Recruitment Visit DW Simpson's website for more info. www.dwsimpson.com/about Casualty JobsProperty & Casualty jobs for Students, Associates & Fellows

 Investment / Financial Markets Old Exam MFE Forum

#1
01-27-2019, 02:58 PM
 thefrumactuary CAS Join Date: Feb 2016 Location: New York City Studying for IFM March 2019 College: Stony Brook University Alumni Favorite beer: Bayesian Posts: 15
Optimal strategy for complicated true/false questions

The goal of this thread is to determine that there is an optimal strategy for guessing on multiple true/false questions

Say a question says

I. Yellow has 6 letters
II. Red has 3 letters
III. Blue has 5 letters

A) I only (not II and not III)
B) II only
C) III only
D) I and II only
E) All are true

that each answer choice is 20 % correct
Now A,D,E -> I is true... P(I) = 60 %
Now B,D,E -> II is true... P(II) = 60 %
Now C,E -> III is true... P(III) = 40 %

Assuming I,II, and III statements are independent
Then P(I)(1 - P(II))(1 - P(III)) = choice A
and
P(I)P(II)P(III) = choice E
based on these probabilities:
A) 60 % * (1 - 60 %) * (1 - 40 %) =
A : 0.144
B : 0.144
C : 0.064
D : 0.216
E : 0.144
Total: 0.712

The exam writers are stuck with 5 choices, so some combinations of {A,B,C} such as {} (not A not B not C) are left out. These excluded probabilities from the sample space result in a Total less than 1. Scaling the probabilities to add to 1:

P(A*) = P(A)/total =

A : 0.2022
B : 0.2022
C : 0.0899
D : 0.3034
E : 0.2022
Total : 1

Therefore by proof of contradiction, there exists an optimal strategy. Just by studying the answer choices, you can come up with a strategy that gets the question right more than 20 % of the time. I would be interested to see if experience proves this right, if we had a large test bank with answers.
#2
01-27-2019, 03:04 PM
 Actuarialsuck Member Join Date: Sep 2007 Posts: 6,131

I didn't read any of that but.... what about the choices I and III only or II and III only?
__________________
Quote:
 Originally Posted by Buru Buru i'm not. i do not troll.
#3
01-27-2019, 03:17 PM
 thefrumactuary CAS Join Date: Feb 2016 Location: New York City Studying for IFM March 2019 College: Stony Brook University Alumni Favorite beer: Bayesian Posts: 15

There would still exist an optimal strategy if:
A) I
B) II
C) III
D) I and II
E) I and III

Assume A,B,C,D,E equal chance of 20 % each
P(I) = 60 %, A,D,E
P(II) = 40 % B,D
P(III) = 40 % C,E

And the math that follows would result in at least one choice being higher
#4
01-27-2019, 03:22 PM
 thefrumactuary CAS Join Date: Feb 2016 Location: New York City Studying for IFM March 2019 College: Stony Brook University Alumni Favorite beer: Bayesian Posts: 15

Quote:
 Originally Posted by Actuarialsuck I didn't read any of that but.... what about the choices I and III only or II and III only?
Interesting: the math would come out to
A : 0.3103
B : 0.1379
C : 0.1379
D : 0.2069
E : 0.2069
Total : 1

 Tags #actuary, #ifm, #logic, #soaprobs

 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 08:57 PM.

 -- Default Style - Fluid Width ---- Default Style - Fixed Width ---- Old Default Style ---- Easy on the eyes ---- Smooth Darkness ---- Chestnut ---- Apple-ish Style ---- If Apples were blue ---- If Apples were green ---- If Apples were purple ---- Halloween 2007 ---- B&W ---- Halloween ---- AO Christmas Theme ---- Turkey Day Theme ---- AO 2007 beta ---- 4th Of July Contact Us - Actuarial Outpost - Archive - Privacy Statement - Top