SOLUTION: An auditor is selecting a sample of 6 tax returns for an audit. If 2 or more of these returns are �improper,� the entire population of 100 tax returns will be audited. What is the

Question 1129718: An auditor is selecting a sample of 6 tax returns for an audit. If 2 or more of these returns are �improper,� the entire population of 100 tax returns will be audited. What is the probability that the entire population will be audited if the true number of improper returns in the population is:
a) 5?
b) 10?
c) 25?
d) 30?
e) Discuss the differences in your results, depending on the true number of improper returns in the population.
I have tried using Hypergeometric Distribution to solve this.
Example:
N (population size) = 100
n (sample size) = 6
A (no. of events of interest in population) = 5 (10, 25, 30 according to the question, Not sure if I got this part correct)
x (no. of events of interest in population) = 2
I have repeated the HypGeo Distribution formula for each part a to d. It looks something like this:
Part a:
[5C2 x (100-5)C(6-2)]/100C6
Part b:
[10C2 x (100-10)C(6-2)]/100C6
Part c:
[25C2 x (100-25)C(6-2)]/10C6
Please advise, thank you!
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Let's start with the following notation for Hyper-Geometric Probability
:
N is the number of items in the population
:
k is the number of items in the population that are classified as successes
:
n is the number of items in the sample
:
x is the number of items in the sample that are classified as successes
:
kCx is the number of combinations of k things, taken x at a time
:
Hyper-geometric probability is the probability that an n-trial hyper-geometric experiment results in exactly x successes, when the population consists of N items, k of which are classified as successes, written as
:
h(x; N, n, k)
:
Note that the probability for 2 or more of the returns are "improper" is calculated using the following equation
:
P(x > or = 2) = 1 -P(x = 0) -P(x=1), where P is probability, gives us
:
P(x > or = 2) = 1 -h(0, N, n, k) -h(1, N, n, k)
:
for part a
:
a. for k = 5, we have
:
P = 1 -h(0, 100, 6, 5) -h(1, 100, 6, 5) = 0.0279
:
that should get you going
:
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