context: It is probably not the case that Lily is white. We believe that Bernhard is gray. Chances are slight that John took the apple. It is unlikely that if Bernhard is gray, or John took the apple, then Julius is a swan. Chances are about even that if John took the apple, and Lily is white, then Greg is yellow. It is likely that if Lily is white, or Bernhard is gray, then Mary got the football.
hypothesis: Chances are about even that either Lily is white, or Mary got the football.
valid_hypothesis: Chances are about even that either Lily is white, or Mary got the football.
invalid_hypothesis: There is almost no chance that either Lily is white, or Mary got the football.
hypothesis_assertion: Either Lily is white, or Mary got the football.