STA 3032  Section 7661 Fall 2011
Assignment 1
This Assignment is worth 50 points and will be
due in class on Friday September
30th
. You are expected to show all work, and explain steps with sentences where necessary.
Assignments must be done in a neat and professional manner. Illegible work will not receive
any credit.
1. The following questions are related to the hypergeometric distribution: a discrete dis
tribution covered in the textbook (Section 5.7) but skipped in class.
(a) A lottery game has the following rules: pick 6 distinct numbers from a set of 49.
The grand prize winner picks 6 numbers out of 6 correctly. Use the fundamen
tal theorem of counting and combinatorics to solve and justify your answers to
questions (i) and (ii):
(i) What is the probability of winning the grand prize?
(ii) What is the probability of getting 4 numbers out of 6 correctly?
(b) Part (a) can also be solved using the hypergeometric distribution. The pmf is
given by
f
(
y
;
k,n,N
) =
P
(
Y
=
y
) =
(
k
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 Fall '08
 Kyung
 Statistics, Probability theory, Hypergeometric Distribution

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