An actuary at Allstate Insurance company determines that there is a 40% probability that there will

An actuary at Allstate Insurance company determines that there is a 40% probability that there will be no claims led at Allstate during the next year. However, provided at least one claim is made, the total amount of claims at Allstate is distributed normally with a mean of 10,000 and a variance of 4,000,000. An actuary at Patton insurance company determines that there is a 60% probability that there will be no claims led at Patton during the next year. However, provided at least one claim is made, the total amount of claims at Patton is distributed normally with a mean of 9,000 and variance of 4,000,000. The claim amounts at Allstate and Patton are independent. Find the probability that in the next year Patton's total claim amount will be greater than Allstate's total claim amount. State your answer to the fourth decimal.

 

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