What is the

Solve analytically.

The Problem: Blue Mountain Property and Casualty Co. (BMP&C) sells, among other products, car insurance. Sue Mountie, a long standing customer, has had a claim in each of the last two years. Underwriting would like to know whether or not to cancel her insurance. An important piece of information: Underwriting doesn't want to insure anyone who has a greater than 1 in 10 chance of having a claim in any given year. Underwriting has asked the actuarial department to determine if 2 consecutive years of claims over the life of the policy is consistent with their underwriting standards, assuming a 40 year life for the policy. In other words, what is the chance of having 2 or more consecutive years with significant claims over a 40 year period, if the probability of a significant claim in a given year is 1/10. What about 3 or more? The Problem: Blue Mountain Property and Casualty Co. (BMP&C) sells, among other products, car insurance. Sue Mountie, a long standing customer, has had a claim in each of the last two years. Underwriting would like to know whether or not to cancel her insurance. An important piece of information: Underwriting doesn't want to insure anyone who has a greater than 1 in 10 chance of having a claim in any given year. Underwriting has asked the actuarial department to determine if 2 consecutive years of claims over the life of the policy is consistent with their underwriting standards, assuming a 40 year life for the policy. In other words, what is the chance of having 2 or more consecutive years with significant claims over a 40 year period, if the probability of a significant claim in a given year is 1/10. What about 3 or more