SOA Exam P Sample Question 201
Study guide: Exam P-1
A group of 100 patients is tested, one patient at a time, for three risk factors for a certain disease until either all patients have been tested or a patient tests positive for more than one of these three risk factors. For each risk factor, a patient tests positive with probability p, where 0 < p < 1. The outcomes of the tests across all patients and all risk factors are mutually independent.
Determine an expression for the probability that exactly n patients are tested, where n is a positive integer less than 100.
- A)
\left[1-3p^2(1-p)\right]^{n-1}\left[3p^2(1-p)\right] - B)
\left[1-3p^2(1-p)-p^3\right]^{n-1}\left[3p^2(1-p)+p^3\right] - C)
\left[1-3p^2(1-p)-p^3\right]\left[3p^2(1-p)+p^3\right]^{n-1} - D)
n\left[1-3p^2(1-p)-p^3\right]^{n-1}\left[3p^2(1-p)+p^3\right] - E)
3\left[(1-p)^{n-1}p\right]^2\left[1-(1-p)^{n-1}p\right]+\left[(1-p)^{n-1}p\right]^3
Answer this question and see the worked solution