4. 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.

Step-by-step explanation:

for n ∈ N

Since Actuary Rahul examines low-risk policies, continuing until a policy with a claim is found and then stopping.

∴ the probability that Actuary Rahul examines exactly n policies

the probability that Actuary Toby examines more than  exactly n policies

Given that policies are actually independent

∴ the probability that the event  (1) and (2) happens simultaneously is

∴  the probability that Actuary Rahul examines fewer policies than Actuary Toby

answer is c

step-by-step explanation:

the answer is (-4,-4)

hope this ! : d