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Comments on Exam 1, Spring 2010
Below are comments on some common mistakes that were made on some of the problems.
Several people had trouble with the counting problems (Chapter 2, especially Section 2.6).
The
topics discussed in Chapter 2 are applied in later material, as we are seeing in Chapter 3 and will
continue to see throughout the course, and they are also important for Exam P.
Of the 149 sample
problems on the SOA website (at
http://www.soa.org/files/pdf/edu-2010-spring-p-ques.pdf
), 31 are
Chapter 2-type counting and/or probability problems; of these, nine are applications of Bayes’ Theorem.
Problem 1:
Part
a
:
Many missed that what was being asked was simply the number of ways to arrange
(permute) 12 distinct objects.
Part
b
:
This needed to be approached as a two-step counting procedure.
Step 1: Count the number of ways to arrange (reserve contiguous shelf space for) the 3 types of
books (namely 3!).
Step 2: Count the number of ways to arrange the books of each type within their allotted space.
To do this, first count the number of ways to arrange (permute) the books of each type among
themselves (5!, 3!, and 4!, respectively), and then use the multiplication rule.
Finally, use the multiplication rule to multiply the results from the two steps to finish.
Problem 2:
This was a partitioning problem (partitioning the set {1, 2, … , 14} of block positions into
three subsets, one for each color), leading to a multinomial coefficient. It can also be done as a product
of three combinations (choose positions for the 5

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