You produce children's' toys and are shopping for product liability insurance. You have conducted very thorough engineering and lab tests of your toys and have calculated hazard rates from toy breakage, incidents from how children interact with them, etc. You have determined that there is a 0.02% chance of a "major" incident occurring with one of your toys in the next year, defined as an incident resulting in $1m in damages.

A. Based on these facts, what is the premium you expect to pay for actuarily fair insurance?

B. After shopping around, you are offered a few premiums that are higher than you expect. Insurers define "major" events the same way but disagree on the probability of one of your toys causing a major event in the next year. They claim this probability is higher. You suspect that prospective insurers lack clear information on how safe your particular toys are.

i. What is this problem called?

ii. What can you do to try to resolve the difference in understanding of this probability? List and describe two for this context.