What would happen to your insurance premium if the probability of houses burning was found to be positively correlated with something and negatively with another?
The correlation between two variables gives the quantitative relationship between them. For example if two variables A and B always occur together, their correlation is equal to 1. On the other hand a correlation of -1 means that if variable A occurs variable B does not.
The probability of a house catching fire could be correlated to several variables, examples of which could be how old a house is, where it is located, the material it is made of and the alike.
As an example assume that an insurance company determines from previous records that a large percentage of houses that caught fire in the past were built over 50 years old. The study also reveals that the proportion of houses built beside a lake was less than houses built elsewhere. This gives a high positive correlation between the age of the house and a high negative correlation between the house being located beside a lake and its catching fire. Now if your house is 52 years old that is likely to increase the premium charged but on the other hand if your house is located beside a lake you are more likely to be offered a lower rate of premium.
The premium paid for an insurance policy is directly proportional to the probability of the event for which the insurance is being taken as determined by the insurance company. To estimate the probability of the event occurring insurance companies use other factors that have been found to either increase or decrease the probability of the event.