SOA Exam P Sample Question 110

Study guide: Exam P-1

The probability of $x$ losses occurring in year 1 is $(0.5)^{x+1}$ for $x=0,1,2,\dots$

The probability of $y$ losses in year 2 given $x$ losses in year 1 is given by the table:

Number of losses in year 1 ( $x$ )	Number of losses in year 2 ( $y$ ) given $x$ losses in year 1
	0	1	2	3	4+
0	0.60	0.25	0.05	0.05	0.05
1	0.45	0.30	0.10	0.10	0.05
2	0.25	0.30	0.20	0.20	0.05
3	0.15	0.20	0.20	0.30	0.15
4+	0.05	0.15	0.25	0.35	0.20

Calculate the probability of exactly 2 losses in 2 years.

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