Question

1

Problem 1 . . Long-term care (LTC) policies are separated into two groups: professional and home care. Dave examines professional care LTC policies, continuing until a policy with a claim is found and then stopping. Atharv follows the same procedure with home care policies. Each professional care policy has a 25% probability of having a claim, and each home care policy has a 30% probability of having a claim. Whether or not one of the two policies has a claim is mutually independent. Calculate the probability that Atharv examines more policies than Dave.

Answer 1

For positive integer n, the probability that Atharv examines exactly n policies is (1-0.3)^n-1 *0.3 =0.7^n-1 *0.3

the probability that Dave examines more than n policies is (1-0.25)ⁿ =0.75ⁿ

since they are mutually independent

The probability that Artharv examines more policies than Dave is

  ,n=1,2,....

Σ0.7"-! * 0.3 * 0.75" 7t

= 0.3/0.7 〉 0.7" * 0.75" n=1

= 0.43 Σ 0.525" n=1 7l

=0.43* 0.525/(1-0.525)

=0.48