It is Known that certain weather events such as thunderstorms, winter storms and high wind have an impact on the occurrence of power outages. Let random variables A denote the number of outages in Arlington and B denote the number of outages in Bethesda in a given day.

In Arlington, the number of power outage has a Poisson distribution with on average 10 outages in a day when the weather is good and on average 12 outages in a day when the weather is bad. Similarly, in Bethesda, the number of power outage has a Poisson distribution with outage rate 5 when the weather is good and 10 when the weather is bad.

Given the weather condition, the outage occurrences in Arlington and Bethesda are independent of each other, that is, A and B are conditionally independent Poisson random variable given the weather condition. Based on the past experience, it is known that 80% of the time the weather is good (that is 80% of the days are "good" days and 20% of the days are "bad" days) in both area.

What is the probability that the number of outages in Arlington is more than the number of outages in Bethesda in a given day?