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Answer:
The probability that Actuary Rahul examines fewer policies that Actuary Toby = 0.2857
Step-by-step explanation:
It is said that Actuary Rahul examines a low risk policy
Probability of a low risk policy having a claim = 10% = 0.1
Actuary Toby examines high risk policy
Probability of a high risk policy having a claim = 20% = 0.2
Let the number of policies examined by actuary Rahul before he finds a claim and stop be n
Probability that actuary Rahul examines exactly n policies =
Probability that Toby examines more than n policies =
Since the claim statuses of policies are mutually independent, the probability that both events happen simultaneously =
probability that both events happen simultaneously =
The probability that Actuary Rahul examines fewer policies that Actuary Toby = =
The probability that Actuary Rahul examines fewer policies that Actuary Toby = 0.2857