SOA Exam P Sample Question 399

Study guide: Exam P-1

In a large population of patients, 20% have cancer. Of those who have cancer, 8% have stage IV cancer.

Patients are tested one at a time, at random, until five patients with stage IV cancer are found.

Let $N$ represent the number of patients tested. Let $C$ represent the number of patients tested who have cancer.

Determine the probability function, $p_{N,C}(n,c)$ , for integers $n$ and $c$ such that $5 \leq c \leq n$ .

A) $p_{N,C}(n,c) = \dfrac{(n-1)!}{(n-c)!(c-5)!4!}(0.8)^{n-c}(0.184)^{c-5}(0.016)^5$
B) $p_{N,C}(n,c) = \dfrac{(n-1)!}{(n-c)!(c-5)!4!}(0.8)^{n-c}(0.12)^{c-5}(0.08)^5$
C) $p_{N,C}(n,c) = \dfrac{n!}{(n-c)!(c-5)!5!}(0.8)^{n-c}(0.184)^{c-5}(0.016)^5$
D) $p_{N,C}(n,c) = \dfrac{(n-5)!}{(n-c)!(c-5)!}(0.8)^{n-c}(0.184)^{c-5}(0.016)^5$
E) $p_{N,C}(n,c) = \dfrac{(n-1)!}{(n-c-1)!(c-4)!4!}(0.8)^{n-c-1}(0.12)^{c-4}(0.08)^5$

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