**Problem 37A**

An insurer issued insurance policies to two independent insureds (Insured #1 and Insured #2). The number of claims in the upcoming year for each insured has a Poisson distribution with mean 1.

- What is the probability that each of the insureds has at least one claim in the upcoming year?
- What is the probability that each of the insureds has at least one claim given that there is at least one claim in the upcoming year among these two insureds?

**Problem 37B**

The number of ambulances passing through a busy intersection (while on duty) in a large city has a Poisson distribution with mean 0.2 per hour. Assume that the number of ambulances passing through this intersection in any given hour is independent of the number of ambulances in any other hour.

As part of a traffic study, this intersection is observed for two one-hour periods (from 9 AM to 10 AM and 1 PM to 2 PM).

- What is the probability that there is at least one ambulance passing through the intersection during these two hours?
- What is the probability that the period of 9 AM to 10 AM has at least one ambulance given that there is at least one ambulance passing through the intersection during these two hours?

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**Answers**

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