SOA Exam P Sample Question 656
Study guide: Exam P-1
A policyholder experiences two sports injuries, each resulting in three possible outcomes: no hospital stay, a short hospital stay, or a long hospital stay.
The joint probability function for i short hospital stays and j long hospital stays is
p(i, j) = \begin{cases}
\dfrac{2!}{i!\,j!\,(2 - i - j)!}(0.2)^i(0.1)^j(0.7)^{2-i-j}, & 0 \le i + j \le 2 \\[6pt]
0, & \text{otherwise.}
\end{cases}Calculate the probability that at least one of the two injuries results in a long hospital stay.
- A)
0.05 - B)
0.15 - C)
0.17 - D)
0.19 - E)
0.36
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