I find the middle phrasing entirely unsatisfactory ("possible" is an obvious replacement)

"Possible" seems to have two distinct meanings. The first one fits your usage, but the other is more of a binary expression, used to express the fact that something is not impossible. In other words, anything whose probability is equal or greater than 1% (say) can be tagged with "possible", and using this sense of "possible" for the 46-55% range seems wrong - it would deserve a stronger word. To avoid the risk of confusion about which sense is meant, I suggest using something like "entirely possible".