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 policies are mutually independent. Calculate the probability that Actuary Rahul examines fewer policies than Actuary Toby.

The probability that Actuary Rahul examines fewer policies than Actuary Toby is 0.2857.

Step-by-step explanation:

It is provided that the 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.

The probability that a low-risk policy has a claim is, P (L) = 0.10.

The probability that a high-risk policy has a claim is, P (H) = 0.20.

For positive integer n, the probability that Actuary Rahul examines exactly n policies is:

P (Actuary Rahul examines exactly n policies) =

The probability that Actuary Toby examines more than n policies is:

P (Actuary Toby examines more than n policies) =

It is provided that  the claim statuses of policies are mutually independent.

Compute the probability that Actuary Toby examines more policies than Actuary Rahul as follows:

Thus, the probability that Actuary Rahul examines fewer policies than Actuary Toby is 0.2857.

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step-by-step explanation:

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