試題詳解

106. Automobile policies are separated into two groups: low-risk and high-risk. Actuary Rahul examines low-risk policies, continuing until a policy with a claim is found and then stopping. Actuary Toby follows the same procedure with high-risk policies. Each low-risk policy has a 10% probability of having a claim. Each high-risk policy has a 20% probability of having a claim. The claim statuses of polices are mutually independent.
Calculate the probability that Actuary Rahul examines fewer policies than Actuary Toby.
(A) 0.2857
(B) 0.3214
(C) 0.3333
(D) 0.3571
(E) 0.4000