How do I solve this probability question?
let's say there are 3 totally independent weather forecast websites. They use totally different ways to predict the weahter. Website 1 says: there's a 55% chance it's gonna rain, Website 2 says: there's a 60% chance it's gonna rain, Website 3 says: there's a 65% chance it's gonna rain.
What would be a correct estimate of the total probability it will rain? You could argue it's 60% because that's the average, but intuitively that sounds wrong to me. Because for example if 1000 websites claim there's a 60% chance it's gonna rain, isn't that prediction more valuable than if 1 website would claim that? What am I missing here?