The problem is as follows:
Tags are used to classify images. An image with the tag "sky" has 90% chance of containing a sunset, with the tag "cloud" giving an image 50% chance of containing a sunset. Given an image with both tags, what is the likelihood that this image contains a sunset? The addition of extra tags should increase the likelihood, i.e. the probability will be at least equal to the highest tag (in this case 90%).
Given the probability of C occurring given A is x, and the probability of C occurring given B is y, what is the probability of C occurring given both A and B have occurred?
The general solution to this seems like something that should be somewhat obvious and easily searchable, but my mind is drawing a blank on what to search for here.